Modelling effects of degree of crystallinity on mechanical behavior of semicrystalline polymers

Viscoplasticity theory based on overstress (VBO) which is one of the unified state variable theories is extended to account for crystallinity ratio () on mechanical behavior of semicrystalline polymers. The modifications on VBO are done considering the semicrystalline polymeric materials somewhat as a composite material since it consists of amorphous and crystalline phases. Amorphous and crystalline phase resistances are arranged in two different analog models: amorphous stiffness and flow are in parallel and series with crystalline phase. Apart from many existing work in the literature, not only uniaxial loading are modeled but also creep and relaxation behaviors are simulated for a hypothetical material. It is shown that when amorphous and crystalline phase resistances acting in parallel are considered in the model, creep, relaxation and uniaxial loading and unloading behaviors can be simulated well using the modified VBO. In addition, uniaxial compression loading and unloading behavior of highly crosslinked ultra-high molecular weight polyethylene (UHMWPE) and creep behavior of polytetrafluoroethylene (PTFE) with different crystallinity ratios are simulated using the proposed VBO model where amorphous and crystalline phases are parallel. Simulation results are compared to the experimental data by Kurtz et al. (2002) and Sun et al. (2005) [Kurtz, S.M., Villarragaa, M.L., Herra, M.P., Bergström, J.S., Rimnacc, C.M., Edidin, A.A., 2002. Thermomechanical behavior of virgin and highly crosslinked ultra-high molecular weight polyethylene used in total joint replacements. Biomaterials 23, 3681–3697; Sun, H., Cooke, R. S., Bates, W. D., Wynne, K.J., 2005. Supercritical CO₂ processing and annealing of polytetrafluoroethylene (PTFE) and modified PTFE for enhancement of crystallinity and creep resistance. Polymer 46, 8872–8882] respectively and good match with experimental data is obtained.     

On a damage law for creep rupture of clays with accumulated inelastic deviatoric strain as a damage measure

To avoid the dependency on origin of time, an improved damage law for creep rupture of clays is proposed considering the accumulated inelastic deviatoric strain as a measure of damage, instead of incorporating time directly. This law is incorporated into an existing anisotropic elastoplastic-viscoplastic bounding surface model for clays. The performance of the damage law was demonstrated via the simulations of creep rupture tests on undisturbed clays, and generally a good agreement between model simulations and test data was obtained. Discussions on the creep rupture parameters were followed and further improvement was suggested. At present when high quality test data for creep rupture is very limited, the proposed damage law could serve as a practical way to model creep rupture of clays.     

Predicting the creep lives of thin-walled cylindrical polymeric pipe linings subject to external pressure

Installation of a close-fitting polymeric thin-walled lining is now standard practice for the rehabilitation of deteriorating gravity pipes. Design of these linings focuses primarily on their ability to resist an external head of groundwater pressure whilst experiencing long-term creep deformations. Existing structural design guidelines are crude and do not provide consistent safety factors. In this paper an existing simple analysis for linear elastic (geometrically non-linear) buckling loads is developed into a time stepping procedure for calculation of the creep lives of time dependent non-linearly elastic systems subject to long-term constant pressure. The results so obtained using different simulations of the creep data obtained for a particular material are then compared with those derived from a set of corresponding physical tests and alternative numerical modelling, and appropriate conclusions are drawn.     

On the viscous and strain rate dependent behavior of polycrystalline NiTi

The viscous and rate dependent behavior of binary, pseudoelastic NiTi is investigated. The main focus is on the decoupling of thermal and viscous effects on the transformation stress level as the specimen material is subject to heating and cooling due to latent heat generation and absorption during phase transition. On this account, an active temperature control is proposed to account for swift temperature variations. In addition to uniaxial testing of the shape memory sample, two-dimensional tension/torsion experiments are conducted in order to generalize the uniaxial findings. Therefore, a two-dimensional strain measuring device is realized, which is capable of measuring large angle strains. Furthermore, the relaxation behavior of the examined NiTi alloy is explored as well.     

Size dependent mechanical behaviour of tantalum

The size dependence of deformation of Ta was studied using compression tests of focused ion beam (FIB) machined microcolumns. Columns with diameters between 0.5 and 8 μm with 〈1 1 1〉 and 〈1 0 0〉 orientations along the column axis were tested. By comparing results of bcc Ta columns with results from previous experiments on fcc metals it was found that Ta shows significantly higher normalized yield stresses in combination with a weaker sample size dependence. The differences between bcc and fcc metals can be attributed to the different dislocation behaviour of bcc metals, especially to the lower mobility of screw dislocations.     

Finite viscoelasticity and viscoplasticity of semicrystalline polymers

Observations are reported on low-density polyethylene in uniaxial tensile and compressive tests with various strain rates and in tensile and compressive relaxation tests with various strains. A constitutive model is developed for the time-dependent response of a semicrystalline polymer at arbitrary three-dimensional deformations with finite strains. A polymer is treated as an equivalent network of chains bridged by junctions (entanglements between chains in the amorphous phase and physical cross-links at the lamellar surfaces). Its viscoelastic behavior is associated with separation of active strands from temporary junctions and merging of dangling strands with the inhomogeneous network. The viscoplastic response is attributed to sliding of junctions between chains with respect to their reference positions. Constitutive equations are derived by using the laws of thermodynamics. The stress–strain relations involve 6 material constants that are found by matching the observations.      

TiNi合金的动态伪弹性行为和率相关相变本构模型

采用万能材料试验机和SHPB实验技术对TiNi形状记忆合金在10-3s-1和102s-1应变率下的伪弹性相变行为进行了实验研究。实验数据表明:TiNi合金的相变过程具有应变率效应,其原因主要是相变阻力受应变率影响应变率越大,相变阻力越大。在三线性热弹性相变模型的基础上,考虑了应变率对相变阻力的影响,并给出了相变阻力的具体形式,建立了一个一维率相关相变本构模型。模型对TiNi合金相变行为的模拟与实验数据吻合较好。     

Annealing and strain rate effects on the mechanical behavior of ultrafine-grained iron produced by SPD

Thermal stability and strain rate sensitivity of ultrafine-grained (UFG) Fe produced by severe plastic deformation (SPD) were investigated. The UFG Fe was processed by equal-channel angular pressing (ECAP) via route Bc. After 6 passes, the grain size of UFG Fe reaches 600 nm, as confirmed by means of electron back scatter diffraction (EBSD). Examination of micro-hardness and grain size of UFG Fe as a function of post-ECAP annealing temperature shows a transition from recovery to recrystallization. The critical transition temperature is approximately 500 °C, and the material has a bimodal structure after annealing at this temperature. Deformation behaviors of ECAP Fe and ECAP + annealing Fe were studied under both quasi-static and dynamic compressive loadings. The UFG iron shows increased strength and reduced strain rate sensitivity compared with its coarse-grained counterparts. The appropriate post-ECAP annealing can increase strain hardening ability and cancel out thermal softening effect with only a small loss of strength under dynamic loading.     

Finite versus small strain discrete dislocation analysis of cantilever bending of single crystals

Plastic size effects in single crystals are investi-gated by using finite strain and small strain discrete dislo-cation plasticity to analyse the response of cantilever beam specimens. Crystals with both one and two active slip sys-tems are analysed, as well as specimens with different beam aspect ratios. Over the range of specimen sizes analysed here, the bending stress versus applied tip displacement response has a strong hardening plastic component. This hardening rate increases with decreasing specimen size. The hardening rates are slightly lower when the finite strain discrete disloca-tion plasticity (DDP) formulation is employed as curving of the slip planes is accounted for in the finite strain formulation. This relaxes the back-stresses in the dislocation pile-ups and thereby reduces the hardening rate. Our calculations show that in line with the pure bending case, the bending stress in cantilever bending displays a plastic size dependence. How-ever, unlike pure bending, the bending flow strength of the larger aspect ratio cantilever beams is appreciably smaller. This is attributed to the fact that for the same applied bend-ing stress, longer beams have lower shear forces acting upon them and this results in a lower density of statistically stored dislocations.     

Size effect on mechanical behavior of random fiber networks

Bonded random fiber networks are heterogeneous on multiple scales. This leads to a pronounced size effect on their mechanical behavior. In this study we quantify the size effect and determine the minimum model size required to eliminate the size effect for given set of system parameters. These include the network density, the fiber length and the fiber bending and axial stiffness. The results may guide the definition of models and the selection of the size of representative volume elements in sequential multiscale models of fiber networks. To underline the origins of the size effect, we characterize the network heterogeneity by analyzing the geometry of the network (density distribution), the strain field and the strain energy distribution. The dependence of the heterogeneity on the scale of observation and system parameters is discussed.     

Combined grain size, strain rate and loading condition effects on mechanical behavior of nanocrystalline Cu under high strain rates

Molecular dynamics simulations of nanocrys-talline Cu with average grain sizes of 3.1 nm, 6.2 nm, 12.4 nm and 18.6 nm under uniaxial strain and stress tension at strain rates of 10 8 s 1 , 10 9 s 1 and 10 10 s 1 are performed to study the combined grain size, strain rate and loading condition effects on mechanical properties. It is found that the strength of nanocrystalline Cu increases as grain size increases regardless of loading condition. Both the strength and ductility of nanocrystalline Cu increase with strain rate except that there is no monotonic relation between the strength and strain rate for specimens under uniaxial strain loading. Moreover, the strength and ductility of specimens under uniaxial strain loading are lower than those under uniaxial stress loading. The nucleation of voids at grain boundaries and their subsequent growth characterize the failure of specimens under uniaxial strain loading, while grain boundary sliding and necking dominate the failure of specimens under uniaxial stress loading. The rate dependent strength is mainly caused by the dynamic wave effect that limits dislocation motion, while combined twinning and slipping mechanism makes the material more ductile at higher strain rates.     

Transient and steady-state nanoindentation creep of polymeric materials

The transient and steady-state nanoindentation creep of polymeric materials was investigated. The creep model is used to explain the experimental data of transient and steady-state creep dominated by viscoelastic deformation and power-law creep deformation, respectively. The Burgers viscoelastic model was used to interpret the transient creep in polymers under nano-indentation. Explicit expression for the displacement of transient creep was derived using the correspondence principle of linear viscoelasticity theory. The power law of strain rate-stress relation was used to explain the creep displacement during the steady state. Three polymers of poly(methyl methacrylate), hydroxyethyl methacrylate copolymer, and the fast-cure acrylic resin were used to measure the nanoindentation creep. The transient creep data are in good agreement with the predictions from the Burgers viscoelastic model. The creep displacement is mainly attributed to the viscous flow of the Kelvin element, and the computed values of viscosities (η_1,c, η_2,c) increase with decreasing preloading rate. By comparing the steady-state creep data with the power law of strain rate-stress relation, the stress exponents for the above polymeric materials were quantitatively determined.     

Surface-effects-dominated thermal and mechanical responses of zinc oxide nanobelts

Molecular dynamics (MD) simulations are carried out to characterize the mechanical and thermal responses of -oriented ZnO nanobelts with lateral dimensions of 21.22 Å×18.95 Å, 31.02 Å × 29.42 Å and 40.81Å × 39.89 Å over the temperature range of 300-1000 K. The Young's modulus and thermal conductivity of the nanobelts are evaluated. Significant surface effects on properties due to the high- surface-to-volume ratios of the nanobelts are observed. For the mechanical response, surface-stress-induced internal stress plays an important role. For the thermal response, surface scattering of phonons dominates. Calculations show that the Young's modulus is higher than the corresponding value for bulk ZnO and decreases by ~ 33% as the lateral dimensions increase from 21.22 Å × 18.95 Å to 40.81 Å × 39.89 Å. The thermal conductivity is one order of magnitude lower than the corresponding value for bulk ZnO single crystal and decreases with wire size. Specifically, the conductivity of the 21.22 Å × 18.95 Å belt is approximately (31-18)% lower than that of the 40.81 Å × 39.89 Å belt over the temperature range analyzed. A significant dependence of properties on temperature is also observed, with the Young's modulus decreasing on average by 12% and the conductivity decreasing by 50% as temperature increases from 300 K to 1000 K.     

Size and strain rate effects in tensile strength of penta-twinned Ag nanowires

Penta-twinned Ag nanowires(pt-AgNWs) have recently attracted much attention due to their interesting mechanical and physical properties. Here we perform largescale atomistic simulations to investigate the influence of sample size and strain rate on the tensile strength of pt-AgNWs. The simulation results show an apparent size effect in that the nanowire strength(defined as the critical stress for dislocation nucleation) increases with decreasing wire diameter. To account for such size effect, a theoretical model involving the interaction between an emerging dislocation and the twin boundary has been developed for the surface nucleation of dislocations. It is shown that the model predictions are in quantitative agreement with the results from atomistic simulations and previous experimental studies in the literatures. The simulations also reveal that nanowire strength is strain-rate dependent, which predicts an activation volume for dislocation nucleation in the range of 1–10b~3,where b is the magnitude of the Burgers vector for a full dislocation.     

A unified residual-based thermodynamic framework for strain gradient theories of plasticity

A unified thermodynamic framework for gradient plasticity theories in small deformations is provided, which is able to accommodate (almost) all existing strain gradient plasticity theories. The concept of energy residual (the long range power density transferred to the generic particle from the surrounding material and locally spent to sustain some extra plastic power) plays a crucial role. An energy balance principle for the extra plastic power leads to a representation formula of the energy residual in terms of a long range stress, typically of the third order, a macroscopic counterpart of the micro-forces acting on the GNDs (Geometrically Necessary Dislocations). The insulation condition (implying that no long range energy interactions are allowed between the body and the exterior environment) is used to derive the higher order boundary conditions, as well as to ascertain a principle of the plastic power redistribution in which the energy residual plays the role of redistributor and guarantees that the actual plastic dissipation satisfies the second thermodynamics principle. The (nonlocal) Clausius-Duhem inequality, into which the long range stress enters aside the Cauchy stress, is used to derive the thermodynamic restrictions on the constitutive equations, which include the state equations and the dissipation inequality. Consistent with the latter inequality, the evolution laws are formulated for rate-independent models. These are shown to exhibit multiple size effects, namely (energetic) size effects on the hardening rate, as well as combined (dissipative) size effects on both the yield strength (intrinsic resistance to the onset of plastic strain) and the flow strength (resistance exhibited during plastic flow). A friction analogy is proposed as an aid for a better understanding of these two kinds of strengthening effects. The relevant boundary-value rate problem is addressed, for which a solution uniqueness theorem and a minimum variational principle are provided. Comparisons with other existing gradient theories are presented. The dissipation redistribution mechanism is illustrated by means of a simple shear model.     

Size dependent response of large shell elements under in-plane tensile loading

Large-scale thin-walled structures with a low weight-to-stiffness ratio provide the means for cost and energy efficiency in structural design. However, the design of such structures for crash and impact resistance requires reliable FE simulations. Large shell elements are used in those simulations. Simulations require the knowledge of the true stress–strain response of the material until fracture initiation. Because of the size effects, local material relation determined with experiments is not applicable to large shell elements. Therefore, a numerical method is outlined to determine the effect of element size on the macroscopic response of large structural shell elements until fracture initiation. Macroscopic response is determined by introducing averaging unit into the numerical model over which volume averaged equivalent stress and plastic strain are evaluated. Three different stress states are considered in this investigation: uniaxial, plane strain and equi-biaxial tension. The results demonstrate that fracture strain is highly sensitive to size effects in uniaxial tension whereas in plane strain or equi-biaxial tension size effects are much weaker. In uniaxial and plane strain tension the fracture strain for large shell elements approaches the Swift diffuse necking condition.     

Specific hardening function definition and characterization of a multimechanism generalized potential-based viscoelastoplasticity model

Given the previous complete-potential structure framework [see Int. J. Plasticity 10(3) (1994) 263], together with the notion of strain- and stress- partitioning in terms of separate contributions of several submechanisms (viscoelastic and viscoplastic) to the thermodynamic functions (stored energy and dissipation), see [Int. J. of Plasticity 17(10) (2001) 1305], a detailed viscoelastoplastic multimechanism characterization of a specific hardening functional form of the model is presented and discussed. TIMETAL 21S is the material of choice as a comprehensive test matrix, including creep, relaxation, constant strain-rate tension tests, etc. are available at various temperatures. Discussion of these correlations tests, together with comparisons to several other experimental results, are given to assess the performance and predictive capabilities of the present model particularly with regard to the notion of hardening saturation as well as the interaction of multiplicity of dissipative (reversible/irreversible) mechanisms.     

Thermo-elastic behavior of a polymeric layer bonded between rigid interfaces

A highly expandable polymeric material have been combined with a stiff skeleton material to form a powerful design of thermal micro-actuators. The bond interfaces with the skeleton laterally restrain deformation of the polymer and consequently direct its volumetric expansion in the transverse direction. A complete lateral constraint at the infinite bond width could maximize the apparent thermal strain of the bonded polymer. However, it is not sure how much strain enhancement can be achieved using a finite bond width. To answer this, we resort to an approximate thermo-elastic model and solve it using the mean-pressure method. This model leads to closed-form solutions to the thermally induced strains and stresses in a bonded polymer layer between rigid interfaces. The closed-form solution shows that the apparent strain of a bonded layer depends on the aspect ratio of the bond width to the layer thickness, besides Poisson’s ratio. Furthermore, it further shows that a bond width five times the thickness of the SU-8 epoxy layer is sufficient to attain 95% of the maximum apparent strain, which is obtained at the infinite width.     

Distribution of dislocation source length and the size dependent yield strength in freestanding thin films

A method is proposed to estimate the size-dependent yield strength of columnar-grained freestanding thin films. The estimate relies on assuming a distribution of the size of Frank-Read sources, which is then translated into a log-normal distribution of the source strength, depending on film thickness, grain size and theoretical strength of the material, augmented with a single fit parameter. Two-dimensional discrete dislocation plasticity (DDP) simulations are carried out for two sets of Cu films and the fit parameter is determined from independent experiments. Subsequent DDP predictions of the stress-strain curves in comparison with the corresponding experimental data show excellent agreement of initial yield strength and hardening rate for films of varying film thickness and grain size. Having thus demonstrated the power of the proposed strength distribution, it is shown that the mode of this distribution governs the most effective source strength. This is then used to suggest a method to estimate the yield strength of thin films as a function of film thickness and grain size. Simple maps are presented that are in very good agreement with recent experimental results for Cu thin films.