POLYETHYLENE

USES AND APPLICATIONS

The effect of installation procedures on the field performance of existing high-density polyethylene (HDPE) pipe used for drainage applications on highway projects was investigated. A total of 45 HDPE pipes were inspected at sites in South Carolina that were statistically selected based on geographical location, pipe diameter, use, and age. The condition of each pipe was not known prior to selection for inspection. Both the external and internal conditions of the pipe were evaluated with respect to AASHTO and ASTM specifications, measurements of pipe deflection with a mandrel set to 5% deflection, and visual inspections of the pipe interior using a video camera. The video camera inspections revealed circumferential cracks in 18% of the pipes, localized bulges in 20% of the pipes, and tears or punctures in 7% of the pipes. Deflections greater than 5% were observed in 20% of the pipes. Installation problems such as poor preparation of bedding soils, inappropriate backfill material, and inadequate backfill cover contributed to the excessive deflection and observed internal cracking in pipes with observed damage. Appropriate construction procedures are essential in achieving a proper installation.

·         Gas Gathering

·         Crude Oil Flow

·         Water Flood

·         Saltwater Disposal

·         Supply Water

·         Fuel Transfer

·         Main Lines

       Fluid and Gas Flow

Polyethylene pipes are used extensively in gas distribution applications worldwide. In USA and Canada over 90% of the natural gas distribution system is in plastics pipes with polyethylene representing 99% of the installations. The use of polyethylene in natural gas distribution systems is growing rapidly.

PE is lightweight, flexible and available in long coils minimizing the number of joints. It is ideally suited for a wide range of service conditions requiring very little maintenance. It has good abrasion resistance, flexible not effected by soil shift and temperature fluctuations.

Polyethylene pipe is recommended by PIPA for use in compressed air installations.

         Fluid Flow

Polyethylene has an extremely smooth surface resulting in a very low coefficient of friction and a minimal loss of head pressure due to frictional losses. This, combined with excellent corrosion and abrasion properties, results in excellent flow characteristics throughout the life of the pipe. for pressurized systems, a Hazen-Williams "C" factor of 150 is used.PE3408/3608 Extra High Molecular Weight (EHMW) Black Pipe - a premium quality, high density, extra high molecular weight, and polyethylene pipe specifically designed for the rigors of the oil field. It is produced from PE3408/3608 resin containing not less than two percent (2%) carbon black for superior resistance to UV degradation. This pipe offers outstanding environmental stress crack resistance (ESCR), the best chemical resistance of any polyethylene pipe and high impact resistance. Polyethylene^® oil field products are available in diameters from 1/2" CTS to 6" IPS coiled and straight lengths from 1/2" through 65" IPS.

           Oil Field

 

A wide selection of HDPE pipe can meet the needs for any oil field applications.Moving fluids through pipe in the oil field demands the utmost in flexibility, reliability and performance. That is why Polyethylene is the best choice for the energy business. High-density polyethylene (HDPE) pipe provides superior flow characteristics, extended life, durability, and reduced maintenance than traditional piping materials, anywhere in the oil patch.

Polyethylene has products specifically for the oil and gas industry for gas gathering, crude transmission, water lines and auxiliary lines.

High Density Polyethylene (HDPE) is available for all pipe applications. Being non-chlorinated, requiring fewer additives, and having a much higher recycling rate, it is considered a more benign plastic than PVC. PVC is more resistant to combustion, but smolders at a lower temperature than HDPE and releases toxic hydrochloric gases before combustion. Cross-linked polyethylene (PEX) is a polyethylene similar in many characteristics to HDPE but with molecules cross-linked to improve its ability to handle higher temperatures. Copper is highly recyclable but copper leaching into water supplies can be harmful to aquatic life. Copper also has significant life cycle problems in its mining, manufacture. Concrete, iron and steel have significant embodied energy usage, and their manufacture is not environmentally benign. However, all of them (with the exception of ABS) are generally considered environmentally superior to PVC.  Aside from concrete, the primary PVC free alternatives are consistent with state government and professional association Environmentally Preferable Purchasing (EPP) guidelines (http://www.apwa.net/Documents/GovtAffairs/Policies/SolidWaste/solid-environpolicy.pdf). Steel, HDPE and copper pipe or conduit may all contain recycled content in the product. Quantities and post consumer content will vary with application and manufacturer. Alternative materials comparison issues The long-term durability of piping systems depends on many factors, including the soil environment, proper installation, material properties such as corrosion resistance, chemical resistance and strength and the performance of joints. Each of the primary PVC free materials has benefits that have kept them as significant market players.Polyethylene will not rust, rot, pit or corrode because of chemical, electrolytic or galvanic action. Chemicals that pose potentially serious problems for polyethylene are strong oxidizing agents or certain hydrocarbons. These chemicals may reduce the pressure rating for the pipe or be unsuitable for transport. Either can be a function of service temperature or chemical concentration. Continuous exposure to hydrocarbons can lead to permeation through the material or electrometric gaskets used at joints. The degree of permeation is a function of pressure, temperature, the nature of the hydrocarbons and the polymer structure of the piping material. The chemical environment may also be of concern where the purity of the fluid within the pipe must be maintained. Hydrocarbon permeation may affect pressure ratings and hinder future connections.

     Water SUPPLIES

The use of plastics pipes in potable water supply applications has been growing rapidly. Both PVC and Polyethylene pipe have major advantages over competitive materials and as polymer technology, keeps improving the choice of plastics pipes for water supply infrastructure projects keeps increasing.

Plastics pipes have design life in excess of 100 years during which they provide excellent performance and trouble free service life. They are corrosion resistant and because of their relatively lightweight are easy to handle, transport and install. Plastics pipes are flexible and fatigue resistant and can withstand repetitive pressure surges. Plastics pipes provide a smooth biological growth free bore through the life of the product eliminating flow restrictions common to other materials.

Water mains typically operate at pressures from 100 to 150 lbs per sq. in. (psi), while distribution lines operate between 40 and 100 psi. Service connection lines are usually a diameter of 1" or less and can be made of various materials: polyethylene, PVC, iron or copper pipe. Currently, PVC has a dominant share of the market for small diameter pipe in the water main (4” - 12”), sanitary sewer and storm sewer (4”-15”) markets, while traditional materials (ductile iron and concrete) continue to have majority market share in the larger diameter pipe. According to the Plastics News (July 16, 2001) the demand for large diameter pipe plastic pipe has increased 8.3% between 1990 and 2000.

The smaller tube sizes used for in building distribution are primarily split between PVC, copper, and iron. There is limited data on the breakdown of market share. Polyethylene is just beginning to penetrate the market for all sizes. The use of galvanized steel and Polyethylene has declined due to corrosion problems with galvanized and catastrophic failures with Polyethylene One of the key design concerns for drinking water infrastructure design and installation is leakage. When one turns on the tap for potable water, there is a cost associated with the acquisition, treatment, and supply (pumping) of the waster. If a water distribution system leaks, the lost water can become an extremely high cost. In arid areas, where costs to acquire water can be exorbitant, leaks can be an expensive proposition. A 4-inch leak in their 24-inch diameter iron pipe can result in the loss of 3 to 5 million gallons of water per day.

HDPE has a slight advantage in leak resistance over PVC. This is because it can be delivered in longer lengths, minimizing the quantity of joints. Furthermore, the butt or electro-fusion processes used to join HDPE provides stronger, tighter, more leak proof joints compared to the bell and spigot joints used in PVC pipe for mains or the solvent glue joints used for smaller distribution. The longer length of HDPE can require longer trenches to be open at a time, but its length and flexibility can allow for trench less procedure, particularly in sewer replacement. HDPE’s greater flexibility and resilience (particularly at lower temperatures) also make it less susceptible to surge and hammer shocks or to damage from digging. HDPE’s flexibility and resilience has made it increasingly popular in earthquake territory or other areas where soils can shift. For larger diameters, the fusion technique requires a fusion machine, which might be problematic in cramped spaces. For smaller diameter pipes, a handheld device can be used to weld/melt the pipe lengths together. Mechanical couplings are available for HDPE, though some of these couplings may be made of PVC.

PEX is another form of polyethylene that retains HDPE’s flexibility and chemical resistance while providing resistance to higher temperatures for which HDPE is not suitable. It is coupled with either fusion techniques or mechanical crimp couplings. Due to its higher temperature ratings it was initially used in radiant and district heating system applications, but is now also beginning to be used more widely in water supply and gas distribution systems.

Ductile Iron (DI) has significantly higher tensile strength, making it more capable of handling higher pressures, crushes and hammer than PVC. DI does not lose strength at high or low temperatures as PVC does. Ductile iron is impermeable to hydrocarbons and other groundwater contamination unlike PVC or other plastic pipe. “There has been much debate over the durability and expected lifespan of each of these materials. The life of a pipe system depends on not only the material, but also the installation and the surrounding environment. All these types of pipe have been on the market for over 30 years, and while there are examples of pipe failures for each of them, this study did not find conclusive evidence to suggest that one material has a significantly different lifespan from the other. When properly designed and installed, pipe systems of any of these materials can be sufficiently durable to withstand many decades of services.”

      Sewerage and Drainage

The use of plastics pipes for both pressure and a gravity sewer is extensive. In addition, there is rapid growth in the use of plastics liners for repair of old and leaking sewer installations.

Availability of large diameter plastics pipes at competitive prices gives design engineers an opportunity to select products on cost and performance basis. Long life expectancy, low maintenance requirements are major advantages in the use of plastics pipes for sewage and drainage applications.

As in water main pipe, HDPE is a comparable alternative to PVC pipe in sewer systems. HDPE sewer pipes are also available in diameters ranging from 4 inches to 36 inches, although for storm sewer, much of the demand is for 10 to 15 inch, while for sanitary 8 to 12 inch are popular diameters. At larger diameters, the major market share is held by concrete, primarily due to cost.

Prior to the 1960s most sewer systems were combined sewers, that is, carried both sanitary and storm water. The system had to be designed to carry large volumes of water during rain events, but otherwise the capacity was little used. In addition, when it did rain the flood of relatively fresh water often negatively impacted water treatment. Design changed so that by the mid 1960s sanitary and storm systems were designed and constructed separately. Storm sewers collect water from roof drains, parking lots and streets. Unlike sanitary sewers, storm wastewater is not typically treated and the flow is directly discharged into a receiving body of water.

Similar to water distribution use, PVC is dominant in the smaller size sewer pipe market with HDPE just beginning to seriously compete. These smaller lines are commonly used in the collection network of subdivisions. In this segment, the competing concrete pipe is non-reinforced concrete pipe in 8" and 10" sections. The smallest diameter reinforced concrete pipe is usually 12" pipe.

The flow formula for smooth pipe should be used to compute the gas flow rate through Polyethylene. It has been found that the Mueller formula for smooth wall pipe describes the flow characteristics of Polyethylene.

3.7       Plumbing

PVC pipes and fittings for plumbing and drainage applications is the choice of plumber’s word wide. Low cost, lightweight, long life expectancy usually for the life of the installation is the overwhelming advantages. PVC does not corrode internally or externally eliminating the possibility of pipe failures or blockages. Cross-linked polyethylene, polypropylene and Polyethylene pipes are used in hot and cold-water reticulation in domestic, commercial and industrial installations. Ease of installation using compression fittings is providing a cost advantage.

Polyethylene, like other plastics, has a thermal coefficient of expansion higher than metals. When subjected to a temperature change, unrestrained (not buried) polyethylene pipe will experience expansion and contraction.

The coefficient of thermal expansion/contraction for Polyethylene is 1.0 x 10^-4 in/in/°F. As a general allowance, 1" per 100' of pipe per 10°F change in temperature.

Forces due to thermal expansion and contraction can be significant. Proper system design should be used to account for the compressive and tension stresses that can be generated.

When pipe is used in pressure applications, the longitudinal stress created by the sum of the bending radius, internal pressure and other stress loads on the pipe should not exceed the material’s design stress rating. Severe but acceptable bends in polyethylene pipelines should be buried or properly restrained.

   Agriculture, Irrigation & Drainage

A variety of alternatives to PVC are used both for water delivery and for drainage. Irrigation sprinkler, drip and drainage systems have long been available in HDPE and have significant advantages in resilience against compression, shovel attack and ground movement. Corrugated steel, concrete and HDPE are all competitive alternatives for drainage.  HDPE drainage pipe is now available in formulations with high-recycled content. Plastic pipe has carved a hunk of the huge market previously dominated by concrete and steel. Highway drainage is a fast growing market for HDPE.  Recently, the Corrugated Polyethylene Pipe Association initiated a third party certification system, which allows for increased acceptance of their product by the American Association of State Highway and Transportation Officials. Footing and under slab drains are all available in HDPE.

           Agricultural and Rural

Water is a lifeline for all farming operations and the security of water is essential. Plastics pipes are available for the wide range of farming applications. Pressure pipes for irrigation, plant watering and potable water reticulation. Non-pressure pipes for irrigation, stock watering, micro-irrigation and general water reticulation systems.

Low cost, wide range of pipe sizes, flexible and easy to handle and transport are all advantages important to the farmers.

    Industrial and Chemical

Corrosion resistance and resistance to attack by many industrial chemicals make plastics pipes the obvious choice for chemical plant installations. Like with all materials used in the construction of chemical plants care must be taken in selecting the correct plastics pipes and fittings that will withstand the operating conditions.

The wide range of polymers used in manufacture of plastics pipes and fittings provide a good range of products from which to select the appropriate material. PVC piping systems are widely used in water, wastewater and chemical transfer. Polyethylene piping systems are well suited to installation in difficult industrial situations. Their high strength and ease of installation also makes them ideal for compressed air reticulation.

  Electrical and Communications

PVC is ideally suited for telecommunication and power conduits due to its high impact strength, smooth internal bore and large range of diameters. Flexibility and corrosion resistance characteristics of PVC conduits make them ideal for a wide range of installation conditions.

High-density polyethylene (HDPE) is ideal for pipe lining and cable encasing, which makes it perfect for communications cables. Although polypropylene pipes are used mainly for plumbing and sewerage applications, they can also be effectively used as conduits.

Advances Ventilation

Advances in Mechanical Ventilation

Basic Principles

The indications for mechanical ventilation, as derived from a study of 1638 patients in eight countries, are acute respiratory failure (66 percent of patients), coma (15 percent), acute exacerbation of chronic obstructive pulmonary disease (13 percent), and neuromuscular disorders (5 percent). The disorders in the first group include the acute respiratory distress syndrome, heart failure, pneumonia, sepsis, complications of surgery, and trauma (with each subgroup accounting for about 8 to 11 percent of the overall group). The objectives of mechanical ventilation are primarily to decrease the work of breathing and reverse life-threatening hypoxemia or acute progressive respiratory acidosis.

Virtually all patients who receive ventilatory support undergo assist-control ventilation, intermittent mandatory ventilation, or pressure-support ventilation; the latter two modes are often used simultaneously. With assist-control ventilation, the most widely used mode, the ventilator delivers a set tidal volume when triggered by the patient's inspiratory effort or independently, if such an effort does not occur within a preselected time.

Intermittent mandatory ventilation was introduced to provide graded levels of assistance. With this mode, the physician sets the number of mandatory breaths of fixed volume to be delivered by the ventilator; between these breaths, the patient can breathe spontaneously. Patients often have difficulty adapting to the intermittent nature of ventilatory assistance, and the decrease in the work of breathing may be much less than desired.

Pressure-support ventilation also provides graded assistance but differs from the other two modes in that the physician sets the level of pressure (rather than the volume) to augment every spontaneous respiratory effort. The level of pressure delivered by the ventilator is usually adjusted in accordance with changes in the patient's respiratory frequency. However, the frequency that signals a satisfactory level of respiratory-muscle rest has never been well defined, and recommendations range from 16 to 30 breaths per minute.

New modes of mechanical ventilation are often introduced. Each has an acronym, and the jargon is inhibiting to those unfamiliar with it. Yet each new mode involves nothing more than a modification of the manner in which positive pressure is delivered to the airway and of the interplay between mechanical assistance and the patient's respiratory effort. The purpose of a new mode of ventilation may be to enhance respiratory-muscle rest, prevent deconditioning, improve gas exchange, prevent lung damage, enhance the coordination between ventilatory assistance and the patient's respiratory efforts, and foster lung healing; the priority given to each goal varies.

Coordinating Respiratory Effort and Mechanical Ventilation

Probably the most common reason for instituting mechanical ventilation is to decrease the work of the respiratory muscles. The inspiratory effort expended by patients with acute respiratory failure is about four times the normal value, and it can be increased to six times the normal value in individual patients. Critically ill patients in whom this increased level of effort is sustained indefinitely are at risk of inspiratory-muscle fatigue, which can add structural injury to already overworked muscles. It is sometimes thought that the simple act of connecting a patient to a ventilator will decrease respiratory effort. Yet unless the settings are carefully selected, mechanical ventilation can actually do the opposite.

With careful selection of ventilator settings, inspiratory effort can be reduced to the normal range. But eliminating inspiratory effort is not desirable because it causes deconditioning and atrophy of the respiratory muscles.Surprisingly, researchers have not attempted to determine the desirable target for reducing inspiratory effort in patients with acute respiratory distress. To reduce effort markedly requires that the ventilator cycle in 

ison with the patient's central respiratory rhythm Figure 1Flow, Airway Pressure, and Inspiratory and Expiratory Muscle Activity in a Patient with Chronic Obstructive Pulmonary Disease Who Received Pressure-Support 

Ventilation at an Airway Pressure of 20 cm of Water.). For perfect synchronization, the period of mechanical inflation must match the period of neural inspiratory time (the duration of inspiratory effort), and the period of mechanical inactivity must match the neural expiratory time. Difficulties in synchronization can arise at the onset of inspiratory effort, at the onset of flow delivered by the ventilator, during the period of ventilator-induced inflation, and at the switch between inspiration and expiration.

Almost all patients who undergo mechanical ventilation receive some form of assisted ventilation, with the patient's inspiratory effort triggering the ventilator. To ensure that the ventilator does not cycle too often, the clinician sets a threshold for airway pressure that will trigger the ventilator. This threshold, referred to as set sensitivity, is usually –1 to –2 cm of water.To reach this threshold, the patient must initiate an inspiratory effort. But when the threshold is reached, inspiratory neurons do not simply switch off. Consequently, the patient may expend considerable inspiratory effort throughout the machine-cycled inflation.

The display of airway pressure and flow tracings on ventilator screens has increased awareness that inspiratory effort is frequently insufficient to trigger the ventilator. At high levels of mechanical assistance, up to one third of a patient's inspiratory efforts may fail to trigger the machine.Surprisingly, unsuccessful triggering is not the result of poor inspiratory effort; indeed, the effort is more than a third greater when the threshold for triggering the ventilator is not reached than when it is reached. Breaths that do not reach the threshold for triggering the ventilator have higher tidal volumes and shorter expiratory times than do breaths that do trigger the ventilator. Consequently, elastic-recoil pressure builds up within the thorax in the form of intrinsic positive end-expiratory pressure (PEEP), or auto-PEEP. To trigger the ventilator, the patient's inspiratory effort first has to generate a negative intrathoracic pressure in order to counterbalance the elastic recoil and then must reach the set sensitivity. The consequences of wasted inspiratory efforts are not fully known, but they add an unnecessary burden in patients whose inspiratory muscles are already under stress.

The inspiratory flow rate is initially set at a default value, such as 60 liters per minute. If the delivered flow does not meet the patient's ventilatory needs, inspiratory effort will increase. Sometimes the flow is increased in order to shorten the inspiratory time and increase the expiratory time, especially in patients with inspiratory efforts that are insufficient to trigger the ventilator. But an increase in flow causes immediate and persistent tachypnea, and as a result, the expiratory time may be shortened. In one study, for example, increases in inspiratory flow from 30 liters per minute to 60 and 90 liters per minute caused increases in the respiratory rate of 20 and 41 percent, respectively.

In studies of interactions between the patient's respiratory effort and mechanical ventilation, remarkably little attention has been paid to the switch between inspiration and expiration. With the use of pressure-support ventilation, ventilatory assistance ceases when the patient's inspiratory flow falls by a preset amount (e.g., to 25 percent of the peak flow). Air flow changes more slowly in patients with chronic obstructive pulmonary disease than in other patients, and patients often start to exhale while the ventilator is still pumping gas into their chests. In 5 of 12 patients with chronic obstructive pulmonary disease who were receiving pressure support of 20 cm of water, expiratory muscles were recruited during ventilator-induced inflation.

Improving Oxygenation and Preventing Lung Injury

A primary goal of mechanical ventilation is to improve arterial oxygenation. Improvement is achieved partly through the use of endotracheal intubation to ensure the delivery of oxygen to the airway and partly through an increase in airway pressure. Satisfactory oxygenation is easily achieved in most patients with airway obstruction. The main challenge arises in patients with alveolar-filling disorders, especially the acute respiratory distress syndrome — a form of noncardiogenic pulmonary edema resulting from severe acute alveolar injury. It has long been recognized that arterial oxygenation can be achieved at a lower inspired oxygen concentration by increasing airway pressure. The goal of using the lowest possible oxygen concentration to achieve an arterial oxygen saturation of approximately 90 percent has not changed in decades. What has changed is how this goal is viewed in relation to other factors, particularly ventilator pressures. In recent years, there has been a growing tendency to be more concerned about high airway pressures than about oxygen toxicity, although this shift has been based on a consensus of opinion rather than on data from studies in patients and animals.

From the outset, clinicians recognized that mechanical ventilation could rupture alveoli and cause air leaks. In 1974, Webb and Tierney showed that mechanical ventilation could also cause ultrastructural injury, independently of air leaks.Their observations went largely unnoticed until a decade later, when several investigators confirmed and extended them. Alveolar overdistention causes changes in epithelial and endothelial permeability, alveolar hemorrhage, and hyaline-membrane formation in laboratory animals

Diffuse infiltrates on chest radiographs originally led clinicians to infer that lung involvement was homogeneous. But computed tomography (CT) reveals a patchy pattern: about one third of the lung is unaerated, one third poorly aerated, and one third normally aerated. A ventilator-induced breath will follow the path of least impediment, travelling preferentially to the normally aerated areas. As a result, these regions are vulnerable to alveolar overdistention and the type of ventilator-induced lung injury found in laboratory animalsFigure 2Lung Injury Caused by Mechanical Ventilation in a 31-Year-Old Woman with the Acute Respiratory Distress Syndrome Due to Amniotic-Fluid Embolism.).

A new era of ventilatory management began in 1990, when Hickling et al.reported that lowering the tidal volume caused a 60 percent decrease in the expected mortality rate among patients with the acute respiratory distress syndrome. In a subsequent trial, Amato et al. randomly assigned patients to a conventional tidal volume (12 ml per kilogram of body weight) or to a low tidal volume (less than 6 ml per kilogram). Mortality was decreased by 46 percent with the lower tidal volume. In a recent study of 861 patients, the Acute Respiratory Distress Syndrome Network confirmed this benefit: mortality was decreased by 22 percent with a tidal volume of 6 ml per kilogram as compared with a tidal volume of 12 ml per kilogram. Lowering the tidal volume, however, failed to improve the outcome in three controlled trials. The discrepant findings can be explained by differences in trial design. Increased survival was demonstrable only when the patients undergoing conventional ventilation had a mean pressure during an end-inspiratory pause (the so-called plateau pressure, a surrogate for peak alveolar pressure) that exceeded 32 cm of water.

The pressures pertinent to ventilatory management are the peak inspiratory pressure, plateau pressure, and end-expiratory pressure. Patients with airway obstruction may have a very high peak pressure without any increase in the plateau pressure. Indeed, the gradient between the two is directly related to the resistance of the airway to airflow. An increase in the peak inspiratory pressure without a concomitant increase in the plateau pressure is unlikely to cause alveolar damage. The critical variable is not airway pressure itself but transpulmonary pressure — airway pressure during the end-inspiratory pause minus pleural pressure. The normal lung is maximally distended at a transpulmonary pressure between 30 and 35 cm of water, and higher pressures cause overdistention. Patients with stiff chest walls, such as those with the acute respiratory distress syndrome due to a nonpulmonary disorder (e.g., abdominal sepsis), have an elevated pleural pressure. In such patients, the airway plateau pressure may exceed 35 cm of water without causing alveolar overdistention.

Clinical decisions based on plateau pressure must take into account the relation between lung volume and airway pressure in the individual patient. The pressure–volume curve in patients with the acute respiratory distress syndrome typically has a sigmoid shape with two discrete bends, called inflection points Figure 3Respiratory Pressure–Volume Curve and the Effects of Traditional as Compared with Protective Ventilation in a 70-kg Patient with the Acute Respiratory Distress Syndrome.).

Some investigators believe that a plateau pressure above the upper bend causes alveolar overdistention. Reducing the tidal volume lowers the plateau pressure, but at the cost of hypercapnia. In a study in which 25 patients with the acute respiratory distress syndrome underwent mechanical ventilation with a tidal volume of 10 ml per kilogram, 20 had a plateau pressure that was 2 to 14 cm of water above the upper bend of the pressure–volume curve.Lowering the plateau pressure to a value that fell below the upper bend required a 22 percent decrease in the tidal volume, causing the partial pressure of carbon dioxide to increase from 44 to 77 mm Hg. The partial pressure of carbon dioxide, in turn, can be decreased by as much as 28 percent by removing tubing and thus decreasing dead space and increasing the frequency of ventilator-induced breaths. By virtue of their stiff lungs, patients with the acute respiratory distress syndrome who do not have an underlying airway obstruction can tolerate a frequency of 30 breaths per minute without gas trapping. Severe hypercapnia can have adverse effects, including increased intracranial pressure, depressed myocardial contractility, pulmonary hypertension, and depressed renal blood flow. The view that these risks are preferable to the higher plateau pressure required to achieve normocapnia represents a substantial shift in ventilatory management.

Lowering the tidal volume is not without hazards. In addition to the potential harm of hypercapnia, the volume of aerated lung may be decreased, with a consequent increase in shunting and worsening oxygenation. One means of minimizing the loss of lung volume is the use of sighs (i.e., single breaths of large tidal volume). In one study, increasing the plateau pressure by at least 10 cm of water during sighs, applied three times a minute over a period of one hour, caused a 26 percent decrease in shunting, with a 50 percent increase in the partial pressure of oxygen. It is unknown whether sighs used at this low frequency cause injury from alveolar overdistention.

The more usual way of improving oxygenation is through the use of PEEP with the intention of recruiting previously nonfunctioning lung tissue. Selecting the right level of PEEP for a given patient with the acute respiratory distress syndrome is difficult, because the severity of injury varies throughout the lungs. PEEP can recruit atelectatic areas but may overdistend normally aerated areas. In a study involving six patients with acute lung injury, for example, the use of PEEP at 13 cm of water resulted in the recruitment of nonaerated portions of lung, with a gain of 320 ml in volume, but three patients had overdistention of already aerated portions of lung, with an excess volume of 238 ml.

Overall, about 30 percent of patients with acute lung injury do not benefit from PEEP or have a fall in the partial pressure of oxygen. With the patient in the supine posture, PEEP generally recruits the regions of the lung closest to the apex and sternum. Conversely, PEEP can increase the amount of nonaerated tissue in the regions close to the spine and the diaphragm.Among patients in the early stages of the acute respiratory distress syndrome, those with pulmonary causes, such as pneumonia, are less likely to benefit from PEEP than are those with nonpulmonary causes, such as intraabdominal sepsis or extrathoracic trauma. This distinction may be related to the type of morphologic involvement: pulmonary causes of the syndrome are characterized by alveolar filling, whereas nonpulmonary causes are characterized by interstitial edema and alveolar collapse. In the later stages of the acute respiratory distress syndrome, remodeling and fibrosis may eliminate this distinction between pulmonary and nonpulmonary causes.
To select the right level of PEEP, some experts recommend bedside calculation of the pressure–volume curve. With the ventilators currently used in the United States, calculating the pressure–volume curve is logistically difficult and technically demanding. Yet many ventilators have a computer screen, and minor software modifications would make it feasible to calculate the curve in as little as two minutes — as with the ventilators available in France. Providing this option on ventilators would increase clinicians' experience with the use of pressure–volume curves in ventilatory management.
Even if the pressure–volume curve is not calculated at the bedside, it is useful to select the PEEP level according to this conceptual framework. A level above the lower bend in the pressure–volume curve is thought to keep alveoli open at the end of expiration and thus prevent the injury that can result from shear forces created by the opening and closing of alveoli. This level of PEEP may also prevent an increase in the amount of nonaerated tissue and, thus, atelectasis. However, the notion that the lower bend signals the level of PEEP necessary to prevent end-expiratory collapse and that pressures above the upper bend signal alveolar overdistention is a gross oversimplification. The relation between the shape of the pressure–volume curve and events at the alveolar level is confounded by numerous factors and is the subject of ongoing research and debate. An understanding of this relation is also impeded by the difficulty in distinguishing collapsed lung units from fluid-filled units on CT.

Most patients with the acute respiratory distress syndrome have an increase in the partial pressure of oxygen when there is a change from the supine to the prone position. In a study of 16 patients, for example, 12 had an increase of 9 to 73 mm Hg in the partial pressure of oxygen, and 4 had a decrease of 7 to 16 mm Hg. The mechanism responsible for the improvement in the partial pressure of oxygen is not clear. The attribution of this improvement to lung recruitment has not been proved. It is now posited that a prone position causes ventilation to be distributed more evenly to the various regions of the lungs, improving the relation between ventilation and perfusion.

Discontinuing Mechanical Ventilation

Because mechanical ventilation can have life-threatening complications, it should be discontinued at the earliest possible time. The process of discontinuing mechanical ventilation, termed weaning, is one of the most challenging problems in intensive care, and it accounts for a considerable proportion of the workload of staff in an intensive care unit.

When mechanical ventilation is discontinued, up to 25 percent of patients have respiratory distress severe enough to necessitate the reinstitution of ventilatory support.61,62 Our understanding of why weaning fails in some patients has advanced considerably in recent years. Among patients who cannot be weaned, disconnection from the ventilator is followed almost immediately by an increase in respiratory frequency and a fall in tidal volume — that is, rapid, shallow breathingFigure 4Tidal Volume, Pleural Pressure, and Pulmonary-Artery Pressure in a Patient Undergoing Assist-Control Ventilation and at the Start and End of a Failed Trial of Spontaneous Breathing.).
 As a trial of spontaneous breathing is continued over the next 30 to 60 minutes, the respiratory effort increases considerably, reaching more than four times the normal value at the end of this period. The increased effort is mainly due to worsening respiratory mechanics. Respiratory resistance increases progressively over the course of a trial of spontaneous breathing, reaching about seven times the normal value at the end of the trial; lung stiffness also increases, reaching five times the normal value; and gas trapping, measured as auto-PEEP, more than doubles over the course of the trial. Before weaning is started, however, the respiratory mechanics in such patients are similar to those in whom subsequent weaning is successful. Thus, unknown mechanisms associated with the act of spontaneous breathing cause the worsening of respiratory mechanics in patients who cannot be weaned from mechanical ventilation.

In addition to the increase in respiratory effort, an unsuccessful attempt at spontaneous breathing causes considerable cardiovascular stress.67 Patients can have substantial increases in right and left ventricular afterload, with increases of 39 and 27 percent in pulmonary and systemic arterial pressures, respectively, most likely because the negative swings in intrathoracic pressure are more extreme. At the completion of a trial of weaning, the level of oxygen consumption is equivalent in patients who can be weaned and in those who cannot. But how the cardiovascular system meets the oxygen demand differs in the two groups of patients. In those who are successfully weaned, the oxygen demand is met through an increase in oxygen delivery, mediated by the expected increase in cardiac output on discontinuation of positive-pressure ventilation. In patients who cannot be weaned, the oxygen demand is met through an increase in oxygen extraction, and these patients have a relative decrease in oxygen delivery.The greater oxygen extraction causes a substantial decrease in mixed venous oxygen saturation, contributing to the arterial hypoxemia that occurs in some patients.

Over the course of a trial of spontaneous breathing, about half of patients in whom the trial fails have an increase in carbon dioxide tension of 10 mm Hg or more. The hypercapnia is not usually a consequence of a decrease in minute ventilation. Instead, hypercapnia results from rapid, shallow breathing, which causes an increase in dead-space ventilation. In a small proportion of patients who cannot be weaned, primary depression of respiratory drive may be responsible for the hypercapnia.

The discontinuation of mechanical ventilation needs to be carefully timed. Premature discontinuation places severe stress on the respiratory and cardiovascular systems, which can impede the patient's recovery. Unnecessary delays in discontinuation can lead to a host of complications. Decisions about timing that are based solely on expert clinical judgment are frequently erroneous.68-70 Several functional measures are used to aid decision making. The level of oxygenation must be satisfactory before one attempts to discontinue mechanical ventilation. Yet in many patients with satisfactory oxygenation, such attempts fail. The use of traditional predictors of the success or failure of attempts — maximal inspiratory pressure, vital capacity, and minute ventilation — frequently has false positive or false negative results. A more reliable predictor is the ratio of respiratory frequency to tidal volume (f/V_T). The ratio must be calculated during spontaneous breathing; calculating it during pressure support markedly impairs its predictive accuracy. The higher the ratio, the more severe the rapid, shallow breathing and the greater the likelihood of unsuccessful weaning. A ratio of 100 best discriminates between successful and unsuccessful attempts at weaning. In a case of clinical equipoise — that is, a pretest probability of 50 percent — an f/V_T of 80, which has a likelihood ratio of 7.5, is associated with almost a 95 percent post-test probability of successful weaning. If the f/V_T is higher than 100, the likelihood ratio is 0.04 and the post-test probability of successful weaning is less than 5 percent.

Several groups of investigators have evaluated the predictive value of f/V_T. Its positive predictive value — the proportion of patients who are successfully weaned among those for whom the ratio predicts success — has generally been high (0.8 or higher). The negative predictive value — the proportion of patients who cannot be weaned among those for whom the ratio predicts failure — has sometimes been reported to be low (0.5 or less). Low negative predictive values have often been reported for patients with a high likelihood of successful extubation — for example, patients undergoing routine postoperative ventilatory assistance and patients who have tolerated initial trials of weaning.

There are four methods of weaning. The oldest method is to perform trials of spontaneous breathing several times a day, with the use of a T-tube circuit containing an enriched supply of oxygen. Initially 5 to 10 minutes in duration, the trials are extended and repeated several times a day until the patient can sustain spontaneous ventilation for several hours. This approach has become unpopular because it requires considerable time on the part of intensive care staff.

The two most common approaches, intermittent mandatory ventilation and pressure support, decrease ventilatory assistance gradually by respectively lowering the number of ventilator-assisted breaths or the level of pressure. When a minimal level of ventilatory assistance can be tolerated, the patient is extubated. The minimal level of assistance, however, has never been well defined. For example, pressure support of 6 to 8 cm of water is widely used to compensate for the resistance imposed by the endotracheal tube and ventilator circuit. A patient who can breathe comfortably at this level of pressure support should be able to tolerate extubation. But if the upper airways are swollen because an endotracheal tube has been in place for several days, the work engendered by breathing through the swollen airways is about the same as that caused by breathing through an endotracheal tube. Accordingly, any amount of pressure support overcompensates and may give misleading information about the likelihood that a patient can tolerate extubation.

The fourth method of weaning is to perform a single daily T-tube trial, lasting for up to two hours. If this trial is successful, the patient is extubated; if the trial is unsuccessful, the patient is given at least 24 hours of respiratory-muscle rest with full ventilatory support before another trial is performed.
Until the early 1990s, it was widely believed that all weaning methods were equally effective, and the physician's judgment was regarded as the critical determinant. But the results of randomized, controlled trials clearly indicate that the period of weaning is as much as three times as long with intermittent mandatory ventilation as with trials of spontaneous breathing. In a study involving patients with respiratory difficulties on weaning, trials of spontaneous breathing halved the weaning time as compared with pressure support in another study, the weaning time was similar with the two methods. Performing trials of spontaneous breathing once a day is as effective as performing such trials several times a day but much simpler. In a recent study, half-hour trials of spontaneous breathing were as effective as two-hour trials.
However, this study involved all patients being considered for weaning, not just those for whom there were difficulties with weaning.

A two-stage approach to weaning — systematic measurement of predictors, including f/V_T , followed by a single daily trial of spontaneous breathing — was compared with conventional management in a randomized trial.
Although the patients assigned to the two-stage approach were sicker than those assigned to conventional weaning, they were weaned twice as rapidly. The rate of complications and the costs of intensive care were also lower with two-stage management than with conventional management.
When patients can sustain spontaneous ventilation without undue discomfort, they are extubated. About 10 to 20 percent of such patients require reintubation.

 Mortality among patients who require reintubation is more than six times as high as mortality among patients who can tolerate extubation. The reason for the higher mortality is unknown; it is not clearly related to the development of new problems after extubation or to complications of reinserting the tube. Indeed, the need for reintubation may simply be a marker of a more severe underlying illness.

In a controlled trial involving patients who could not sustain spontaneous ventilation, the patients who were extubated and then received noninvasive ventilation through a face mask had a shorter mean overall period of ventilatory support (10.2 days) than those who remained intubated and were weaned by decreasing pressure support (16.6 days).Although this result is promising, it is not clear how many such patients or which ones could benefit from this approach.

Other Approaches to Mechanical Ventilation

Noninvasive ventilation, an approach that is becoming more widespread, was reviewed in the Journal in 1997. Two new approaches under investigation are liquid ventilation and proportional-assist ventilation they have not yet been approved for general clinical use.

 

Mechanical Annealing

A new regime for mechanical annealing and strong sample-size strengthening in body centred cubic molybdenum

Abstract

Because of crystal symmetry, body centred cubic (BCC) metals have large differences in lattice friction between screw and edge dislocations, and manifest generally different mechanical behaviours from face centred cubic (FCC) metals. Although mechanical annealing (significant drop in stored dislocation density in response to applied stress) has been observed in FCC metals, it has not been observed in BCC metals so far. Here we show that significant mechanical annealing does occur in BCC Mo pillars, when their diameters decrease to hundreds of nanometers. In addition, there exists a critical diameter for focused ion beam milled pillars, below which the strengthening exponent increases dramatically, from ~0.3 to ~1. Thus, a new regime of size effects in BCC metals is discovered that converges to that of FCC metals, revealing deep connection in the dislocation dynamics of the two systems.

Introduction

The deformation behaviour of small-volume metals, in particular the effects of sample size (that is, the diameter D of micro- and nano-pillars) on the apparent strength σ, has been attracting considerable attention recently 

 . 

A number of studies of single-crystal micro- and nano-pillars have demonstrated the 'smaller is stronger' trend, with the flow stress increasing markedly with decreasing sample size. The strength appears to follow an empirical power law, scaling with D as D^−α. Although it is generally believed that dislocation source limitation is responsible for the D dependence, the exact origin of the size effect remains a subject of intense debate .Particularly interesting are the behaviours of BCC metals, which in bulk form tend to exhibit significant deviations from FCC metals. Molybdenum (Mo) is a representative and widely studied example of such BCC metals.

The behaviour of Mo pillars is intriguing in two aspects. First, investigations so far indicate BCC Mo pillars exhibit a relatively weak sample-size dependence at room temperature. In an extreme case of Mo-alloy pillars produced by high-temperature eutectic solidification followed by chemical etching, the samples were believed to be initially dislocation free, and the flow stress was reported to be independent of the pillar size. In focused ion beam (FIB) micro-machined pillars, α was found to be <~0.45 for Mo by several groups, considerably lower than those for FIBed FCC metallic pillars. This major difference has been postulated to be related to the known difference in the mobility of screw dislocations. The Peierls barrier of screw dislocation is much higher than those of non-screw dislocations in BCC metals, so the mobility of screw dislocation is exceptionally low and strain rate-controlling in conventional plasticity of BCC metals, whereas, in FCC metals, the Peierls barrier is low as well as similar for screw and non-screw dislocations. It is known that the athermal shear stress for screw dislocation motion in Mo is 750 MPa (the corresponding uniaxial stress would be of the order of 1.5 GPa) near 0 K . At stresses far above this level, such that the free-flight dislocation velocity is exceedingly high, for example, approaching the speed of transverse acoustic wave, the mobility difference between edge and screw dislocations is expected to diminish. This trend was confirmed by our molecular dynamics (MD) simulation. As shown in Figure 1, a dislocation loop developed into a track-field-like geometry, when the external applied shear stress was fixed at 1.5 GPa. However, when the externally applied shear stress was increased to 4 GPa, the dislocation loop kept a roughly round shape instead during its expansion. According to the tenet of 'smaller is stronger', for sufficiently small pillar size and, therefore, high enough prevailing stress, the dislocation dynamics and, hence, the size dependence in BCC metals could become more similar to that in FCC pillars.

Figure 1: Effect of stress level on dislocation loop expansion at 20 K from MD simulations.

a) The loop developed into a track-field-like geometry when the external applied shear stress was fixed at 1.5 GPa, consistent with the traditional understanding that screw dislocations move much slower than edge dislocations. (b) When the externally applied shear stress was increased to 4 GPa, the dislocation loop kept a roughly round shape during its expanding process. This means that the mobility of the screw and edge segments now becomes similar under such high stresses. 

 

Second, mechanical annealing has not been experimentally observed in Mo even though the concept of mechanical annealing does not contradict Weinberger and Cai's simulation in which a single screw dislocation can be pushed out of the pillar without self-breeding at lower stresses (<5.5 GPa in D=36 nm pillar). Mechanical annealing refers to the reduction of dislocation density in the deforming volume, when dislocation generation and accumulation is outweighed by dislocation annihilation and escape from the surfaces. For FCC pillars below a certain D_C, mechanical annealing renders the pillar almost dislocation free. In contrast, in Mo. This has been rationalized by MD simulations of Mo pillars as due to dislocation self-multiplication at higher stresses (>5.5 GPa in D=36 nm pillar), arising from the cross-kinks generated along the screw dislocations that have non-coplanar core structure. Many in the community believe that mechanical annealing is not possible for BCC metals regardless of sample size. pillars pillars, it has been shown that dislocation tangles are retained even after extensive plastic deformation

In this work, we investigate these two issues by in situ transmission electron microscope (TEM) compression of FIBed Mo pillars over a wide D range that includes smaller sizes than those accessed before. We uncovered three different stress regimes, in which explosive dislocation nucleation through dislocation self-multiplication (high-stress regime, HSR), mechanical annealing (medium-stress regime, MSR) or bulk-like plasticity (low-stress regime, LSR) dominates, respectively. We also demonstrate and explain that there is a marked change in α not only for BCC versus FCC pillars, but also for BCC pillars in different D regimes.

Results

Mechanical annealing in Mo

Figure 2 shows one typical example of the <111> oriented pillars. In this case, the starting pillar had D~142 nm at the free end, 660 nm in height and a sidewall taper angle of about 4° with a high density of FIB-induced surface defects (Fig. 2a). The TEM bright-field images here, Figure 2a through Figure 2e, are still frames extracted from the movie recorded during the nanocompression test, in one-to-one correspondence with the five points (a through e) marked in its engineering stress versus strain curve displayed in Figure 2f. In this work, the engineering stress was defined as the instantaneous force divided by the smallest cross-sectional area just before the structural collapse. Admittedly, this will underestimate the stress before the collapse point. For example, if we plot the instantaneous contact stress versus strain, there will be no more 'strain hardening' (Supplementary Fig. S1). However, this convention will make sure the collapse stress is always the true stress, which is the main focus of this work.

Figure 2: Mechanical annealing during the in situ nanocompression test of a typical Mo nanopillar.

 

Bright-field TEM images of the diameter D=142 nm pillar before (a) and after (e) the in situ compression test. (b), (c), (d) and (e) correspond to the marked points in the engineering stress versus strain curve in (f). The scale bar in each figure represents 100 nm. See also the recorded video in Supplementary Movie 1.

Dislocations were found to emerge from the contact interface (heterogeneous dislocations sources) between the pillar and the punch, and accumulate near the free end even before the apparent 'yield' point b in Figure 2f, in LSR. Beyond this point (that is, getting into MSR), the ensuing plastic deformation cleans up the dislocations in the regions near the free end, except at the location in immediate contact with the interface. Presumably, this is due to the friction confinement between the diamond tip and the pillar. Apparently, mechanical annealing did occur and continued through stages c and d. Serrations are obvious in the curve (for example, at points c and d in Fig. 2f). They are due to intermittent shear along certain slip planes in the 'cleaned up' region, a phenomenon often seen during the plastic flow in small pillars. The stress is observed to reach a value near 4 GPa (HSR) before the structural collapse at point d. The evolution of the pillar together with the responsible dislocation activities can be better visualized in Supplementary Movie 1.

The cleaned region (Fig. 2d) after mechanical annealing looks rather like the pristine Mo achieved by high-temperature formation or annealing^{4, 12}, in the sense of lacking 'obvious' dislocation lines ('obvious' defined here by the contour length of a dislocation being a significant fraction of D) or dislocation forest inside. But one cannot tell whether some point defects or tiny point-defect clusters still remain in the cleaned region, as they are beyond the resolution of conventional TEM. It is quite likely that mechanical annealing can only achieve partial cleaning-up compared with bona fide, and the strong size dependence of the collapse strength is consistent with that. high-temperature thermal annealing. Certainly, Ga solutes may escape as gas during high-temperature thermal annealing, but unlikely to do so during mechanical annealing, so the chemical implantation induced by FIB is unlikely to be cleaned away by mechanical annealing. Consequently, our mechanically annealed region is still not as structurally perfect as the high-temperature processed pillars near the melting point

The subsequent collapse of mechanically annealed region (Fig. 2d,e) and those in previous works may result from the onset of the dislocation self-multiplication as described . However, it is worth noting that the predicted critical stress in ref 5. for smaller pillars (with obvious mechanical annealing observed experimentally) marks the upper bound instead of lower bound of the measured strength. This is because the dislocation density (after mechanical annealing) falls on the left side of the saddle point in the stress versus dislocation density curve.

In short, the starting material (FIBed pillar) contained high density of defects and the stress was ramped up gradually. The time sequence was LSR → some dislocation breeding by surface emission and Frank-Read mechanism (Fig. 2b) → MSR → mechanical annealing (Fig. 2c,d) → dislocation-free region created in Figure 2d (no 'obvious' dislocations in the region) → HSR → the dislocation-free region collapsed by explosive dislocation self-multiplication → the system unloaded and passed through MSR to LSR. However, the system unloaded very quickly and spent very little time in MSR. In thermal annealing, the annealing time (typically minutes to hours) is as important as the annealing temperature. If the time-at-temperature is very short, it is quenching instead of annealing, and quenching preserves defects. The same is true for mechanical annealing: because of the high stress-quench rate, there is insignificant mechanical annealing, so the system unloaded to zero stress (Fig. 2e) with a lot of quenched-in dislocations as 'fossil record' of the HSR explosive dislocation self-multiplications.

Strong sample-size strengthening

Similar behaviour of mechanical annealing and eventual structural collapse was repeatedly observed in other Mo pillars with D<200 nm. Another example is the D=80 nm pillar shown in Supplementary Figure S2 (see also Supplementary Movie 2). For this group of pillars, their representative engineering stress-strain curves are displayed in Figure 3a. For comparison, the curves for D>200 nm pillars are displayed in Figure 3b where discrete strain bursts are also noticeable, consistent with previous reports on similar-sized Mo pillars by Greer et al.nd Arzt et al.But due to their larger sizes, mechanical annealing should be less obvious; or rather, the effect of mechanical annealing is counterbalanced by dislocation creation inside by more traditional means 

Figure 3: Representative engineering stress–strain curves of Mo nanopillars.

(a) Diameter D<200 nm, including 80 nm (red), 120 nm (green), 165 nm (blue), 172 nm (orange) and 185 nm (purple). (b) Diameter D>200 nm, including 268 nm (green), 369 nm (blue), 463 nm (yellow), 607 nm (red), and 1,200 nm (purple).

  

The maximum flow stress sustainable in each pillar before the final collapse, σ_f, is plotted in Figure 4a as a function of D. An obvious sample-size effect is observed, with σ_f clearly increasing with decreasing D. There appears to be two size regimes, corresponding to the two groups of pillars in Figure 3a,b. For the group with D>~200 nm, the D dependence of σ_f is relatively weak. Plotting logσ_f versus logD, we obtain the slope α~0.3, as shown in Figure 4b. This α is consistent with that found in previous reports (α=0.22 to 0.45, for a similar D-range). In contrast, a dramatically different slope (about 3 times larger) is observed when the pillar sizes were reduced to below D_C=200 nm. Similar trend was obtained, if the flow stress values were taken at a fixed strain (for example, at 5% strain, as done by some groups for other metal pillars. The relatively low data scatter of the σ_f of our smaller pillars (<~200 nm), where mechanical annealing reduced dislocation density down to ~0, seems to be consistent with the previous observation that dislocation-free crystals tend to show smaller data scatter.

 

 

Figure 4: Sample-size strengthening of Mo nanopillars.

 

 

(a) Maximum flow stress before collapse plotted as a function of pillar diameter D (black dots), showing two regimes with apparently different Dσ₀; see blue and red lines for larger and smaller diameter regimes, respectively). Green line is the fit of experimental data using equation (1). (b) Double-log plot showing two different α values, 1.0 and 0.29 for red and blue lines, respectively.

dependences (power law fits without considering

Discussion

In the following, we present a simple analysis to rationalize the two seemingly different regimes, and explain the previously noted difference between BCC and FCC metals. For the different α, previous arguments invoked the difference in screw dislocation mobility through the lattice as the possible cause. However, they do not explain exactly how this would result in a α much smaller for BCC metals than for FCC metals. Also, as noted earlier, for very small Mo pillars, the prevailing stresses are far above the athermal threshold stress for single screw motion; this would partly diminish the difference in the mobility of screw and edge dislocations as discussed in Figure 1. In general, the observed strength is not simply controlled by lattice friction to dislocation motion. Instead, to match the imposed strain rate, the dislocations need to multiply, similar to the dislocation source limited deformation in small-volume FCC pillars. As shown by Weinberger and Cai for BCC Mo, at sufficiently high stresses above a critical stress, σ_c, the cross-kink debris (loops) left behind the moving screw dislocations can open up, becoming sources of dislocations themselves. This self-multiplication overwhelms the annihilation (mechanical annealing), resulting in an outburst of dislocations to mediate the dramatic shape change (Fig. 2e), that is, the collapse. The HSR–MSR boundary σ_c is therefore the σ_f plotted in Figure 4. σ_f can be modelled by modifying the σ_c expression of Weinberger et al. into 

 

Here σ₀ is the lattice friction contribution to flow stress from screw dislocation's high-speed motion through the lattice accompanying the sample collapse. σ₀ is taken to be 1.3 GPa, which is almost the same as the average yield stress for 4% pre-strained Mo pillars with size of ~1,200 nm and the flow stress for 11% pre-strained Mo pillars regardless of pillar diameter 

 . The second term, which brings in the D dependence, is the stress needed for the dislocation to execute self-multiplication by bow-out, which becomes operative at HSR in lieu of the double-kinks mechanism. Here G is the shear modulus; b is the Burgers vector. The source size is assumed to scale with D, and the scaling factor is accounted for by the fitting parameters, β and B. The fit using equation (1), as shown by the green line in Figure 4a, represents the experimental data fairly well, and gives β=1.83 and B=0.109 nm.

At very small D, the second term in the bracket in equation (1) is much larger than unity, such that the former can be dropped. In this case, in a logσ_f–logD plot, the D dependence is governed by the 1/D term, giving α~1. In other words, σ₀ is only a small part of the very high σ_f for these small pillars such that the effective D-sensitivity is large. In contrast, when D is relatively large, σ₀ becomes a significant part of the σ_f so that the effective D-sensitivity gets weaker. If one then continues to assume a D^−α power law (in lieu of equation (1)), the slope in a log σ_f−log D plot would give an effective α significantly lower than 1 (α~0.3 in Fig. 4b). Therefore, the general size dependence, equation (1), can be approximated by two size regimes represented by two different simple power-law dependences on D, as shown in Figure 4b. The two corresponding power-law fits to the σ_f−D data are drawn in Figure 4a, exhibiting the different D sensitivities as expected.

The magnitude of σ₀ does make a difference in controlling the apparent α, even when the observed strength is actually mostly dislocation-source-controlled. The large magnitude of σ₀ for BCC Mo renders the second size regime (weaker D dependence) obvious, once the D surpasses a couple of hundred nanometers. In comparison, for FCC metals σ₀ is known to be much smaller. As a result, the D dependence remains stronger for a large D range. The same is also true for some BCC metals such as Nb, for which room temperature is already close to the critical temperature at which thermal fluctuation energy can overwhelm the Peierls barrier to produce a relatively small σ₀. Figure 1 shows that simply reaching the athermal threshold or even σ₀ is not enough to eliminate the mobility difference between the screw and edge dislocations. This is because the latter is fully accomplished only in the limit that the dislocations possess velocities approaching the transverse acoustic wave velocity, thus requiring extraordinarily high stresses near the ideal strength; at lower velocities and stresses, the screw dislocations always possess mobility advantage owing to their non-planar cores. Therefore, the transition to become FCC-like requires a very small size (for example, D<~200 nm), when the stress eventually reaches sufficiently high levels.

Methods

Sample preparation

The starting material we used was a directionally solidified bulk Mo single crystal. The as-received crystal was ~10 mm in diameter and 3 mm in height, with the axis along <111> direction. Several pieces of samples with their dimension of 0.5 mm×2 mm×2.5 mm were cut by electric-discharge machining with the edge of the length direction oriented along <111> direction. The samples were then mechanically thinned to 0.05 mm in thickness and subsequently electro-polished at the middle part of a selected edge (2.5 mm) using a solution of 60% Methanol, 35% 1-Butanol and 5% HClO₄. One selected sample was then mounted carefully onto a copper substrate used for in situ TEM nanocompression test. The edges (2 mm) of the sample was aligned carefully so that the axis of those later fabricated pillars will be the <111> crystal orientation. More details about the sample preparation method are described in the work by Shan et al. The FIB cutting in this work was performed through three steps, from rough machining to fine milling and eventually to final superfine polishing, as illustrated in Supplementary Figure S3a–c. The beam current was reduced to 1.5 pA at the last milling step to minimize FIB damage. Pillars with diameters from 75 to 1,200 nm were obtained with their taper angles ranging from 2 to 4.5° The systematic variation of pillar diameter allows the determination of the sample-size dependence of strength in the nanoscale regime not accessed in previous studies. The final diameters and heights of the pillars were measured using s.e.m.

Experimental methods

In situ compression tests were performed in a JEOL JEM-2100F TEM using the Hysitron PI95 PicoIndenter with a flat diamond punch (tip diameter ~1 μm). The compression tests were conducted at a constant displacement rate in the range of 2 to 5 nm s⁻¹. The engineering stress σ was calculated as σ=4F/πd², where F is the measured force and d is the contact diameter before collapse. The engineering strain ɛ was calculated as ɛ=ΔL/L₀, where ΔL is the compression displacement and L₀ is the initial pillar height.

MD simulation methods

Large scale parallel molecular dynamics program LAMMPS and visualization program AtomEye , z=180×[111] with periodic boundary condition in x and z directions and free surface in y direction. Dislocation loop with Burgers vector b=1/2[111] was introduced by shifting the upper slab with respect to the lower slab by a Burgers vector along z direction and was relaxed by conjugate gradient relaxation method. All simulations were carried out under the NPT (constant atom number, external pressure and temperature) ensembles with temperature T=20 K, P_xx=0.0 GPa and P_zz=0.0 GPa. Shear stress τ_yz was realized through adding a constant force to each atom in the several atomic layers of upper and lower free surface. A time step of 1 fs was used during the integrating of Newton's equation of motion.