Post-yield Strain Research Articles

Effects of non-enzymatic glycation on cancellous bone fragility

Post-translational modifications of collagen, such as non-enzymatic glycation (NEG), occur through the presence of extracellular sugars and cause the formation of advanced glycation end-products (AGEs). While AGEs have been shown to accumulate in a variety of collagenous human tissues and alter the tissues' functional behavior, the role of AGEs in modifying the mechanical properties of cancellous bone is not well understood. In this study, an in vitro ribosylation model was used to examine the effect of NEG on the mechanical behavior of cancellous bone. Cancellous bone cores and individual trabeculae were harvested from the femoral heads of eight fresh human cadavers and paired for ribosylation and control treatments. The cores were subjected to either unconfined compression tests or were demineralized and subjected to stress relaxation tests. The trabeculae were loaded to fracture in four-point bending. In vitro NEG significantly reduced the energy dissipation characteristics of the organic matrix as well as the post-yield properties including the stiffness loss of the individual trabeculae ( p < 0.05) and the damage fraction of cancellous bone ( p < 0.001). AGEs in cancellous bone cores from both treatment groups correlated with damage fraction ( r 2 = 0.36, p < 0.05) and post-yield strain energy ( r 2 = 0.21, p < 0.05); and with energy dissipation characteristics of the organic matrix ( r 2 = 0.35, p < 0.05). In the control group, AGEs content increased up to six-fold with age ( r 2 = 0.95, p < 0.008). This study shows that cancellous bone is susceptible to NEG that increases its propensity to fracture. Moreover, despite tissue turnover, cancellous bone may be susceptible to an age-related accumulation of AGEs.

Stress and Strain Analysis of Pipelines with Localized Metal Loss

This paper presents the analysis of stress and strain data acquired with the finite element method and with tests that used post-yielding strain gages bonded onto the external surface of pipes that suffered thickness metal loss and that had been loaded with internal pressure. These metal loss areas were produced by three different processes: actual internal corrosion, careful machining of external patches by spark-erosion, and milling of internal or external patches to simulate limited or extensive strip corrosion defects with depths up to 70% of the pipe’s thickness. Results show that: (1) the extensive longitudinal internal or external defect areas behave as extensive strips with a high degree of freedom to deform elastically and plastically in the circumferential and thickness directions, and (2) large restraints are offered to the longitudinal strains by the non-corroded thick walls parallel to the strip. Using the above experimental observation, a simple mathematical model was developed to predict the burst pressure of pipes with longitudinal extensive and reasonably constant depths of metal loss. This model employed thin-pipe-strength-of-material equations associated to a bulging correction factor, the material’s uniaxial ultimate strength and the von Mises criterion. The onset of plastic collapse predicted by the simple model was successfully compared with results determined from actual hydrostatic tests that were carried out with full scale pipe specimens and from finite element results generated by the use of a commercial program. The developed model was also helpful in showing that the yield and burst behaviors of new or corroded pipeline specimens under laboratory test conditions can be directly compared and extended to the yield and burst behaviors of buried pipeline in field operation.

PART 3: BURST TESTS OF PIPELINE WITH EXTENSIVE LONGITUDINAL METAL LOSS

The first paper of the present series appearing in Experimental Techniques highlighted the increased need and opportunity for applying experimental techniques in the field of pipeline integrity.1 The series’ second paper 2 presented the analysis of strain data acquired by using postyield strain gages bonded inside the metal loss areas of different pipe specimens loaded with internal pressure. It was concluded that longitudinal strains undergo very little change in magnitude after the yielding of the material, whether the rosette is located on the surface of a nondefective specimen, or if placed in the nominal specimen area located some distance from the defect. Elastic and plastic results show that points located in the metal loss areas of specimens with extensive longitudinal defects are highly free to deform elastically and plastically in the circumferential and thickness directions. At those points, much resistance is offered to the longitudinal strains by the thick walls parallel to the metal loss strip, as can be noticed by the small longitudinal strain values.

A simple elastoplastic hardening constitutive model for EPS geofoam

Expanded polystyrene (EPS) geofoam is increasingly being used as a construction material of choice in situations where its mechanical properties—such as its extremely low density, volume contraction under deviatoric compressive loading, and existence of post-yielding strain hardening—can be exploited. In this paper, a simple elastoplastic hardening constitutive model of EPS geofoam is formulated to model the mechanistic behaviour of EPS geofoam taking into account the characteristic properties of EPS. The model is based on experimental results from a series of triaxial tests performed on EPS samples for confining pressure ranging from 0 to 60 kPa at room temperature (23 °C). Behaviour under higher temperatures is currently under investigation and will be addressed in a future publication. The model has a total of six independent parameters and can be calibrated from data obtained from triaxial tests. It is shown that the constitutive model is able to correctly replicate the characteristic behaviour of the EPS geofoam under shearing. The model is relatively simple to incorporate into numerical codes for geotechnical analysis.

Relaxation phenomenon in epoxy glass aged under post‐yield strain

AbstractRelaxation phenomenon in epoxy glass aged under shear strain larger than an upper yield point was studied. After aged under post‐yield strain for various aging periods, cylindrical specimens of epoxy glass were twisted clockwise (in the same direction as the prestrain) or counterclockwise (the opposite direction to the direction of the prestrain). The evolution of yield points was significantly different from that of the specimens aged under preyield strain. There exist two knee‐like yield points on stress–strain curves of specimens twisted counterclockwise: one evolved toward to an upper yield point and merged the other knee‐like yield point whose stress value was almost independent of aging time. On the basis of the experimental results, we proposed a combined relaxation model of two relaxation mechanisms: one is relaxation results in an isotropic structure whose center in stress space is the stress value in the terminal zone and the other is kinetic relaxation of the isotropic center. The combined relaxation indicated the possibility of phase transition caused by postyield strain, and therefore the higher yield stress than that of an annealed specimen was not resulted from strain‐accelerated aging, but presumably resulted from a structural change under postyield strain. POLYM. ENG. SCI. 46:630–634, 2006. © 2006 Society of Plastics Engineers

Relationship Between Bone Morphology and Bone Quality in Male Tibias: Implications for Stress Fracture Risk

Biomechanical properties were assessed from the tibias of 17 adult males 17-46 years of age. Tissue-level mechanical properties varied with bone size. Narrower tibias were comprised of tissue that was more brittle and more prone to accumulating damage compared with tissue from wider tibias. A better understanding of the factors contributing to stress fractures is needed to identify new prevention strategies that will reduce fracture incidence. Having a narrow (i.e., more slender) tibia relative to body mass has been shown to be a major predictor of stress fracture risk and fragility in male military recruits and male athletes. The intriguing possibility that slender bones, like those shown in animal models, may be composed of more damageable material has not been considered in the human skeleton. Polar moment of inertia, section modulus, and antero-posterior (AP) and medial-lateral (ML) widths were determined for tibial diaphyses from 17 male donors 17-46 years of age. A slenderness index was defined as the inverse ratio of the section modulus to tibia length and body weight. Eight prismatic cortical bone samples were generated from each tibia, and tissue-level mechanical properties including modulus, strength, total energy, postyield strain, and tissue damageability were measured by four-point bending from monotonic (n = 4/tibia) and damage accumulation (n = 4/tibia) test methods. Partial correlation coefficients were determined between each geometrical parameter and each tissue-level mechanical property while taking age into consideration. Significant correlations were observed between tibial morphology and the mechanical properties that characterized tissue brittleness and damageability. Positive correlations were observed between measures of bone size (AP width) and measures of tissue ductility (postyield strain, total energy), and negative correlations were observed between bone size (moment of inertia, section modulus) and tissue modulus. The correlation analysis suggested that bone morphology could be used as a predictor of tissue fragility and stress fracture risk. The average mechanical properties of cortical tissue varied as a function of the overall size of the bone. Therefore, under extreme loading conditions (e.g., military training), variation in bone quality parameters related to damageability may be a contributing factor to the increased risk of stress fracture for individuals with more slender bones.

Modeling tensile response and flow localization effects in 316SS after exposure to spallation and fission irradiation environments

The mechanical stability of structural materials under irradiation is a major concern for reactor component design and life cycle evaluation. The most important issue is the loss of ductility due to the development of radiation damage defect structures in the material. The acute loss of material tensile ductility is often characterized by a process where the material necks at very low uniform elongations in tensile loading, just following the yield point, a process commonly referred to as flow localization. The process where small tensile strains lead to plastic instability is examined through the analysis of tensile test data for 316SS irradiated either in a fission neutron spectrum or in a mixed proton and neutron spectrum characteristic of spallation sources. In both cases, it is found that uniform elongation levels are limited by a critical material strength. It is shown that there is a direct correlation between the material yield strength and the uniform elongation for the materials examined here. It is also shown that the large differences in He and H production between the two kinds of radiation environments have little or no effect on tensile properties. A further implication of the work is that the specifics of the post-yield flow and strain hardening processes are less important than the critical stress for determining the onset of plastic instability.

Modeling tensile response and flow localization effects in selected copper alloys

Radiation-induced defect structures are known to elevate material yield strength and reduce material ductility. Together, these changes substantially reduce uniform elongation compared to the unirradiated material condition so that the small strains induce plastic instability. This process, commonly known as flow localization, is examined here for selected copper alloys and compared to similar response in 316SS. It is found that uniform elongation levels are limited by a critical material strength which is independent of the irradiation damage state. This result establishes that the details of the post-yield flow and strain hardening processes are less important than the critical stress for controlling plastic instability. In the case of OFHC Cu, post-irradiation heat treatment restores some initial ductility, but also reduces the critical stress for incipient flow localization.

Tensile properties of a tempered martensitic iron–chromium–carbon model alloy

A detailed study of the strain-hardening on a Fe–9Cr–0.1C tempered martensitic model alloy has been undertaken in the temperature range of 77–343 K. The true stress–true strain curves were calculated from tensile test data. In the framework of a phenomenological model for the strain-hardening based on dislocation mechanics, it has been shown that, above 170 K, the whole post-yield behavior can be reasonably described by a single law. On the contrary, below 170 K, a careful examination of the strain-hardening indicated that the single law cannot describe anymore the entire post-yield strain range. It has been suggested that this behavior is related to the low mobility of the screw dislocations in the low temperature regime that influences the shape of the tensile curve.

An experimental investigation of the large-strain tensile behavior of neat and rubber-toughened polycarbonate

The large-strain tensile behavior of polycarbonate and polycarbonate filled with several volume fractions ( f) of rubber particles is studied via an optical technique. Digital image correlation is used to determine, in two dimensions, the local displacement gradients and full-field displacements during a uniaxial tension test. Full-field strain contours, macroscopic true stress–strain behavior, and local volumetric strain are reduced from the raw test data. Full-field strain contours exhibit a decreasing degree of localization with increasing f. The true stress–strain results show a decrease in modulus, yield stress, post-yield strain softening, and subsequent strain hardening with increasing f. The volumetric strain decreases with increasing f as well. In the case of the neat polymer, comparisons are made to a three-dimensional finite element simulation.

Tensile yield in compact bone is determined by strain, post-yield behaviour by mineral content

Compact bone specimens from many species were examined to determine the relationships, in tension, between mineral content, Young's modulus, yield stress, yield strain, post-yield stress, post-yield strain, ultimate stress, ultimate strain and work under the stress–strain curve. Yield strain varied much less than the post-yield strain, and yield stress was strongly dependent on Young's modulus. Mineral content was a rather poor predictor of yield stress. However, post-yield events were predicted better by mineral (calcium) content than by Young's modulus. The greater the mineral content the less the post-yield work under the curve and the less the increase in post-yield stress and strain. The findings are compared with those of Les et al . who compressed specimens from equine metacarpals. Where they can be compared, the results are consistent with each other.

Role of collagen and other organics in the mechanical properties of bone.

Relevant mechanical properties of bone The mechanical properties of bone material are determined by the relative amounts of its 3 major constituents: mineral, water, and organics (mainly type I collagen); by the quality of these components; and by how the resulting material is arranged in space. For our purposes, the mechanical properties of bone can be summed up as follows: modulus of elasticity, yield stress and yield strain, post-yield stress and post-yield strain, and the total area under the stress-strain curve. Also important are some fracture mechanics properties, but these are not discussed here. A typical tensile stress-strain curve for a bone specimen is shown in Fig. 1. The modulus of elasticity shows how stiff the bone material is. Indeed, stiffness is the prime property of bone, distinguishing it from tendon, which has much less tensile stiffness, almost no shear stiffness, but which is nearly as strong and is much tougher. Yield stress and strain determine how much energy can be absorbed before irreversible changes take place. Post-yield stress and strain determine mainly how much energy can be absorbed after yield but before fracture. Irreversible changes take place at yield, caused by microdamage. The total area under the stress-strain curve is equivalent to the work that must be done per unit volume on the specimen before it breaks. Fracture mechanics properties show the extent to which bone is resistant to crack initiation and to crack travel (which are different things and governed by somewhat different features). In fact, crack travel resistance is given rather well by post-yield stress and strain.

Localisation phenomena in glassy polymers: influence of thermal and mechanical history

The macroscopic deformation behaviour of amorphous polymers is dominated by localisation phenomena like necking and crazing. Finite element simulations show that the details of the intrinsic post-yield behaviour, strain softening and strain hardening, determine the severity of strain localisations. In order to perform these numerical simulations an accurate constitutive model is required. The compressible Leonov model is, for this purpose, extended to include temperature effects. Experimentally it is demonstrated that by a small increase in strain softening (by annealing of polycarbonate) or substantial decrease (by mechanical rejuvenation of polystyrene), transitions from ductile to brittle and, respectively, brittle to ductile can be realised. An analytical stability analysis is performed that predicts stable or unstable neck growth dependent on the ratio between yield stress and hardening modulus. The extensive simulations and experimental results lead to the conclusion that in order to macroscopically delocalise strain, and thus improve toughness, one has to reduce strain softening or enhance strain hardening, either by improving the intrinsic behaviour of polymers, or by creating an optimised micro-structure.

Post-failure behavior of two mine pillars confined with backfill

Researchers from the National Institute for Occupational Safety and Health used a series of instruments (borehole extensometers , earth pressure cells , and embedment strain gauges) to study the post-failure behavior of two pillars confined by backfill in a test section at the Buick Mine near Boss, MO, USA. Evaluation of these pillars was part of a research project to assess the safety of the test section when high-grade support pillars were mined. Data from borehole extensometers installed in several backfill-confined pillars and numerical modeling indicated that these pillars failed during extraction of the support pillars. Failure was corroborated by the post-yield pillar strain response in which the immediate elastic strain was negligible compared to the time-dependent strain component measured between blasting rounds. A three-dimensional, finite-element program with an elastic perfectly plastic material model was calibrated using extensometer data to estimate rock mass modulus and unconfined compressive strength . The resulting rock mass modulus was 45–60% of the average deformation modulus obtained from laboratory tests, and the calibrated compressive strength was 40% of average laboratory values. A rock mass modulus equal to 52% of the average laboratory deformation modulus was calculated using the rock mass rating (RMR) system. Rock mass strength was calculated with the generalized Hoek–Brown failure criterion for jointed rock and indicated that in situ strength was 33% of laboratory strength. Post-failure stresses calculated by the finite-element model were larger for confined pillars than post-failure stresses in unconfined pillars calculated using empirical plots. Data from the calibrated model provided a strain-hardening stress-versus-strain relationship. This knowledge is critical for the design of mines that use partially failed pillars to carry overburden load.

A theory of amorphous solids undergoing large deformations, with application to polymeric glasses

This paper develops a continuum theory for the elastic–viscoplastic deformation of amorphous solids such as polymeric and metallic glasses. Introducing an internal-state variable that represents the local free-volume associated with certain metastable states, we are able to capture the highly non-linear stress–strain behavior that precedes the yield-peak and gives rise to post-yield strain softening. Our theory explicitly accounts for the dependence of the Helmholtz free energy on the plastic deformation in a thermodynamically consistent manner. This dependence leads directly to a backstress in the underlying flow rule, and allows us to model the rapid strain-hardening response after the initial yield-drop in monotonic deformations, as well as the Bauschinger-type reverse-yielding phenomena typically observed in amorphous polymeric solids upon unloading after large plastic deformations. We have implemented a special set of constitutive equations resulting from the general theory in a finite-element computer program. Using this finite-element program, we apply the specialized equations to model the large-deformation response of the amorphous polymeric solid polycarbonate, at ambient temperature and pressure. We show numerical results to some representative problems, and compare them against corresponding results from physical experiments.

On the transition toughness of two RA martensitic steels in the irradiation hardening regime: a mechanism-based evaluation

An analysis of the transition fracture toughness and constitutive behavior of F82H and Eurofer97 reduced activation martensitic steels are presented in both unirradiated and irradiated conditions. The unirradiated toughness data for F82H show very steep temperature dependence and the Eurofer97 toughness data measured with 5 mm versus 10 mm thick specimens are systematically higher. Both of these observations indicate a loss of constraint. Constraint loss adjustments are applied using a three-dimensional finite element analysis based toughness scaling model. The adjusted F82H results can be represented by a master curve (MC) and the corresponding 5 and 10 mm adjusted data fall in the same scatter band. The 10 mm irradiated specimens, with generally lower toughness levels, suffer minimal constraint loss. The irradiation induced MC T 0 shifts (Δ T 0) are analyzed in terms of changes in constitutive properties. The Δ T 0 are generally consistent with the observed irradiation hardening. However, the effects of irradiation on post-yield strain hardening behavior must be considered to obtain self-consistent hardening-shift relations.

Accelerated aging studies of UHMWPE. I. Effect of resin, processing, and radiation environment on resistance to mechanical degradation.

The resin and processing route have been identified as potential variables influencing the mechanical behavior, and hence the clinical performance, of ultra-high molecular weight polyethylene (UHMWPE) orthopedic components. Researchers have reported that components fabricated from 1900 resin may oxidize to a lesser extent than components fabricated from GUR resin during shelf aging after gamma sterilization in air. Conflicting reports on the oxidation resistance for 1900 raise the question of whether resin or manufacturing method, or an interaction between resin and manufacturing method, influences the mechanical behavior of UHMWPE. We conducted a series of accelerated aging studies (no aging, aging in oxygen or in nitrogen) to systematically examine the influence of resin (GUR or 1900), manufacturing method (bulk compression molding or extrusion), and sterilization method (none, in air, or in nitrogen) on the mechanical behavior of UHMWPE. The small punch testing technique was used to evaluate the mechanical behavior of the materials, and Fourier transform infrared spectroscopy was used to characterize the oxidation in selected samples. Our study showed that the sterilization environment, aging condition, and specimen location (surface or subsurface) significantly affected the mechanical behavior of UHMWPE. Each of the three polyethylenes evaluated seem to degrade according to a similar pathway after artificial aging in oxygen and gamma irradiation in air. The initial ability of the materials to exhibit post-yield strain hardening was significantly compromised by degradation. In general, there were only minor differences in the aging behavior of molded and extruded GUR 1050, whereas the molded 1900 material seemed to degrade slightly faster than either of the 1050 materials.

Influence of nonenzymatic glycation on biomechanical properties of cortical bone

In this study, the influence of nonenzymatic glycation (NEG) on the mechanical properties of bone and bone collagen were investigated. Bovine cortical bone specimens were incubated in ribose to cause collagen cross-links in vitro, and nondestructive mechanical testing was used to determine tensile and compressive elastic modulus as a function of incubation time. Mechanical properties associated with yield, postyield, and final fracture of bone were determined at the end of the incubation period. The stiffness of the collagen network was measured using stress relaxation tests of demineralized bone cylinders extracted periodically throughout the incubation period. It was found that accumulation of nonenzymatic glycation end-products in cortical bone caused stiffening of the type I collagen network in bone (r 2 = 0.92; p < 0.001) but did not significantly affect the overall stiffness of the mineralized bone ( p = 0.98). The ribosylated group had significantly more NEG products and higher yield stress and strain than the control group ( p < 0.05). Postyield properties including postyield strain and strain energy were lower in the ribosylated group but were not significantly different from the control group ( p = 0.24). Compared with the control group, the ribosylated group was characterized by significantly higher secant modulus and lower damage fraction ( p < 0.05). Taken together, the results of this study suggest that collagen in bone is susceptible to the same NEG-mediated changes as collagen in other connective tissues and that an increased stiffness of the collagen network in bone due to NEG may explain some of the age-related increase in skeletal fragility and fracture risk.

A physically based constitutive model for a V–4Cr–4Ti alloy

A constitutive model for low-to-intermediate temperatures, strains, and strain rates is developed for the program heat of V–4Cr–4Ti. The basic form of the model is derived from more general dislocation-based models of yield stress and strain hardening. The physically based forms are fit to a database derived from tensile tests carried out over a wide range of temperatures and strain rates. Yield and post-yield strain-hardening contributions to the flow stress are additive. The yield stress has both thermally activated and athermal components. The former is described by a two-mechanism activated dislocation slip model, with contributions that appear to arise from both lattice friction (at lower temperatures) and dislocation pinning by interstitial impurities (at higher temperatures). The yield stress data can be correlated using a strain rate-compensated temperature. The model uses a temperature-weighted average of the two mechanisms. Post-yield strain hardening was found to be approximately athermal. Strain hardening is fit to a two-component modified Voce-type saturating flow stress model. The constitutive model is also used to determine the flow stability limits as estimates of uniform tensile strains. The relatively compact, but mechanism-based, semi-empirical model has a number of both fundamental and practical advantages that are briefly outlined.

A general framework for the mechanical behaviour of clays

It is suggested that the structure of clays may be distinguished simply as either ‘sedimentation’ or ‘post-sedimentation’, depending on whether gross yield in one-dimensional compression in void ratio-vertical effective stress plane occurs on the original sedimentation compression curve or to the right of this curve. A behavioural framework is proposed for clays having either of these structures, the magnitude of the strength sensitivity St when consolidated to the gross yield state (in compression) quantifying the effects of structure. The behaviour of natural clay consolidated to stress states pre-gross yield is related to the undisturbed clay sensitivity St; the gross yield curve is generally of arch shape, its size relative to that of the reconstituted clay depending on this sensitivity. Clays having St &gt; 1 consolidated to stresses beyond gross yield exhibit post-gross yield behaviour in which values of sensitivity reduce with increasing post-yield strain. It is found that following normalization for composition (using the stress ratio at critical state M), volume (using p*e) and structure (using the sensitivity at gross yield St ), many different clays have the same gross yield curve. A basically frictional linear flow rule is found to operate from small or medium to large strains for both natural and reconstituted clays.