Logarithmic Strain Research Articles

Anisotropic plasticity‐damage material model for sheet metal — Regularised single surface formulation

AbstractSheet metal forming as well as mechanical joining demand increasingly accurate and efficient material modelling to capture large deformations, the inherent sheet orthotropy and even process‐induced damage, which is expected to be influential. To account for large strains the additive logarithmic strain space is utilised that enables a straightforward incorporation of plastic anisotropy, herein modelled by a Hill48 yield function. A gradient‐enhancement is used to equip the ductile damage model with an internal length scale curing the damage‐induced localisation. An affine combination of the local and non‐local softening variable is derived enabling a more efficient single surface formulation for the regularised plasticity‐damage material model.

Spatial Rigid-Flexible-Liquid Coupling Dynamics of Towed System Analyzed by a Hamiltonian Finite Element Method

An effective Hamiltonian finite element method is presented in this paper to investigate the three-dimensional dynamic responses of a towed cable-payload system with large deformation. The dynamics of a flexible towed system moving in a medium is a classical and complex rigid-flexible-liquid coupling problem. The dynamic governing equation is derived from the Hamiltonian system and built-in canonical form. A Symplectic algorithm is built to analyze the canonical equations numerically. Logarithmic strain is applied to estimate the large deformation effect and the system stiffness matrix will be updated for each calculation time step. A direct integral solution of the medium drag effect is derived in which the traditional coordinate transformation is avoided. A conical pendulum system and a 180° U-turn towed cable system are conducted and the results are compared with those retraced from the existing Hamiltonian method based on small deformation theory and the dynamic software of Livermore software technology corp. (LS-DYNA). Furthermore, a circularly towed system is analyzed and compared with experimental data. The comparisons show that the presented method is more accurate than the existing Hamiltonian method when large deformation occurred in the towed cable due to the application of logarithmic strain. Furthermore, it is more effective than LS-DYNA to treat the rigid-flexible-liquid coupling problems in the costs of CPU time.

A Finite Element Study to Investigate the Mechanical Behaviour of Unidirectional Recycled Carbon Fibre/Glass Fibre-Reinforced Epoxy Composites.

Recycled carbon fibre–reinforced epoxy (rCF/EP) composites and recycled glass fibre–reinforced epoxy (rGF/EP) composites were numerically investigated to examine their mechanical properties, such as uniaxial tensile and impact resistance, using finite element (FE) methods. The recycled composites possess unidirectional, long and continuous fibre arrangements. A commercially available Abaqus/CAE software was used to perform an explicit non-linear analysis with a macroscale modelling approach, assuming the recycled composites as both homogenous and isotropic hardening. Five composite types were subjected to a numerical study based on the recycled fibre’s volume fraction (40 and 60%) of rCF/EP and rGF/EP, along with (100%) fibreless cured epoxy samples. The materials were defined as elastoplastic with a continuum ductile damage (DUCTCRT) model. The experimental tensile test results were processed and calibrated as primary input data for the developed FE models. The numerical tensile results, maximum principal stress and logarithmic strain were validated with their respective experimental results. The stress–strain curves of both results possess a high accuracy, supporting the developed FE model. The numerical impact tests examined the von Mises stress distribution and found an exponential decrease in the stiffness of the composite types as their strength decreased, with the 60% rCF/EP sample being the stiffest. The model was sensitive to the mesh size, hammer velocity and simulation time step. Additionally, the total internal energy and plastic dissipation energy were measured, but were higher than the experimentally measured energies, as the FE models eliminated the defects from the recycled process, such as a poor fibre wettability to resin, fibre bundle formation in rCFs and char formation in rGFs. Overall, the developed FE models predicted the results for a defect-free rCF/EP and rGF/EP composite. Hence, the adopted modelling techniques can validate the experimental results of recycled composites with complex mechanical properties and damage behaviours in tensile and impact loading conditions.

Nonlinear thermodynamic phase field theory with application to fracture and dynamic inelastic phenomena in ceramic polycrystals

A geometrically nonlinear phase field theory accounting for dissipation, rate effects, nonlinear thermoelasticity, fracture, and other structural changes is constructed in the context of continuum thermodynamics. First, a general framework accommodating arbitrary strain energy potentials, inelastic deformation kinematics, and unlimited order parameters is formulated. Next, the framework is specialized to account for deformation physics pertinent to crystalline ceramics and minerals deformed at high rates and high pressures. Notably, a logarithmic elastic strain tensor referred to an intermediate material configuration enters the nonlinear thermoelastic potential. Order parameters represent fractures, solid–solid phase transformations, deformation twinning, or slip of partial dislocations. Thermodynamically consistent kinetics manifest in equations reminiscent of Ginzburg–Landau dynamics, wherein viscosity coefficients are most generally state- and rate-dependent. Pressure-dependent strength commensurate with frictional resistance is enabled in alternative kinetic equations for dynamic fracture with irreversibility constraints. Linearization of the model suitable for moderate volume changes but small deviatoric elastic strain and rotation is undertaken. The theory is applied to study deformation and failure of polycrystalline forms of boron carbide (B4C), titanium diboride (TiB2), and a B4C-TiB2 ceramic composite. Solutions are derived and evaluated numerically for uniaxial stress tension and compression, uniaxial strain compression, and planar shock compression. The latter analysis yields relationships among viscosity coefficients, gradient regularization lengths, and characteristics of steady plastic waveforms. Results give new insight into high-rate deformation mechanisms previously speculated in these materials.

Dynamic Shearing Resistance of an Energetic Material Simulant: Sucrose

Sucrose is a commonly used energetic material simulant for β-HMX. However, its behavior under extreme loading conditions remains poorly understood. Pressure-Shear Plate Impact (PSPI) experiments have been conducted to provide an experimental foundation for developing a suitable constitutive model for sucrose. Experiments have been performed at two different nominal normal stress values, 3 and 9.5 GPa, with nominal shear strain-rates of the order of 106s−1. Sucrose exhibits a shear strength of ∼400-500 MPa in this pressure range, with a relatively small pressure sensitivity. However, pronounced strain softening is observed in sucrose at sufficiently large shear strains - even a dramatic drop in shearing resistance in some cases. A thermodynamically-consistent constitutive theory is presented to model the thermoelastic, thermo-viscoplastic response of sucrose. The use of the logarithmic strain and an appropriate set of invariants allows for separation of the Cauchy stress into pressure and deviatoric terms. A complete Mie-Gruneisen equation of state is presented to model the volumetric behavior while the deviatoric response is captured through the Johnson-Cook Model. The material model is able to capture experimental observations and predicts localization in the form of adiabatic shear bands, which explains the catastrophic drop in shearing resistance of sucrose observed in the experiments. Such localization events carry important implications for energetic materials in the context of hot-spot formation and underline the importance of dynamic shearing strength measurements.

An Extended Three-Dimensional Finite Strain Constitutive Model for Shape Memory Alloys

AbstractA 3D finite-strain constitutive model for shape memory alloys (SMAs) is proposed. The model can efficiently describe reversible phase transformation from austenite to self-accommodated and/or oriented martensite, (re)orientation of martensite variants, minor loops, latent heat effects, and tension–compression asymmetry based on the Eulerian logarithmic strain and the corotational logarithmic objective rate. It further accounts for smooth thermomechanical response; temperature dependence of the critical force required for (re)orientation, temperature, and load dependence of the hysteresis width; and asymmetry between forward and reverse phase transformation, and it is flexible enough to address the deformation response in the concurrent presence of several phases, i.e., when austenite, self-accommodated, and oriented martensite co-exist in the microstructure. The ability of the proposed model to describe the aforementioned deformation response characteristics of SMAs under multiaxial, thermomechanical, and nonproportional loading relies on the set of three independent internal variables, i.e., the average volume fraction of martensite variants, their preferred direction, and the magnitude of the induced inelastic strain, which further allow for an implicit description of a fourth internal variable, the volume fraction of oriented as opposed to self-accommodated martensite. The calibration of the model and its numerical implementation in an efficient scheme are presented. The model is validated against experimental results associated with complex thermomechanical paths, including tension/compression/torsion experiments, and the efficiency of its numerical implementation is verified with simulations of the response of a biomedical superelastic SMA stent and an SMA spring actuator.

Large Deformation Dynamic Analysis of a Cable System by a New Hamiltonian Finite Element Method

This paper develops a new Hamiltonian nodal position finite element method for dynamic analysis of spatial flexible cable systems with large deformation. The dynamic governing equation is derived from finite elasticity theory. Logarithmic strain is applied to construct large deformation Hamiltonian canonical equations. An efficient second-order symplectic difference algorithm is built to solve the canonical equations numerically. A large strain conical pendulum system is analyzed numerically by the proposed method, and the numerical results are compared with those retracted from the existing Hamiltonian methods and Livermore Software Technology Corporation: dynamics (LS-DYNA). The proposed method is further verified by two tethered dynamic experiments involving large displacement motion and large deformation. The comparisons and verifications demonstrate that the proposed method is of symplectic conservation, has high accuracy and has stability for calculating flexible cable system dynamics with large deformation.

MBW 1200 – Hot Stamping Steel with Increased Ductility

Hot stamping steels are trending towards increased ductility without sacrificing too much stiffness. Thus a new aluminum silicon coated grade, MBW 1200 + AS has been developed, with typical yield strength after hot stamping and paint baking of YS ≈ 1000 MPa, tensile strength TS ≈ 1200 MPa and A80 > 5.0 %. The highly increased ductility compared to 22MnB5 expresses through the particularly increased bending angle of >75° and the logarithmic true thickness strain of ≈0.90. Hence MBW 1200 shows the desired significantly higher ductility compared to 22MnB5 in lateral crash testing without crack appearance. The process stability has been approved by different tests, e.g. increased furnace dwell time, tool temperature and transfer time. Verifying MBW 1200 in patchwork blank applications with total thicknesses of 3.0 and 3.5 mm showed only a minor decrease of YS and TS between 30 and 50 MPa and leaves the Vickers hardness at ≈400 HV10 with fully martensitic microstructure. In partial press hardening tests, using tools heated of up to 550 °C, bending angles reach the test’s maximum and YS falls below 500 MPa with a hardness of ≈210 HV1. Finally in a comparison between experiment and numerical hot stamping simulation it can be shown, that the determined material modelling parameters can well be used in the feasibility analysis of new automotive components.

Development of dynamic constitutive model of epoxy resin considering temperature and strain rate effects using experimental methods

Epoxy resin composite materials are increasingly used in the aerospace field. The dynamic mechanical behavior of the resin matrix is of great significance in studying the impact response of composites. In the current study, the quasi-static and dynamic compression properties of TDE86 epoxy are studied at different temperatures, and the influence of the temperature and strain rate on the mechanical properties of epoxy are analyzed. The quasi-static and dynamic compression stress–strain curves are used to fit the parameters of the Zhu–Wang–Tang (ZWT) constitutive equation at different temperatures. A subroutine for the ZWT constitutive model is developed in ABAQUS, and numerical simulations of split Hopkinson pressure bar tests are performed. The results show that, at low strain rates, the elastic modulus, yield stress, and yield strain of the epoxy increase as the strain rate increases and decrease as the temperature increases. The dynamic stress–strain curve of the epoxy can be divided into four stages, namely the initial elastic, yield, strain softening, and unloading stages. There is no distinct relationship between the yield strain and the logarithmic strain rate under high strain rates, although the yield strain is generally smaller than that under low strain rates. The yield stress increases linearly with the logarithmic strain rate. Under the same strain rate, the yield stress decreases as the temperature increases, whereas the yield strain does not change monotonically. By comparing the stress–strain curves obtained by simulations with the test results, the developed subroutine is validated and the applicability of the ZWT constitutive model at different temperatures is verified.

Transition from engineering strain to the true strain in analytical description of metals hardening

Purpose of the work is related with the impossibility of correctly estimating the strain hardening of metals (alloys) in the area of their large total deformations due to absence of additivity in the traditionally used value of engineering strain g, its nonlinear change in the area of large values, and absence of data in the technical literature Hall-Petch coefficient Ai for logarithmic true deformations, which led to the task of correct transition from the values of the engineering strain 0 < g < 50...60 % to the value of the true logarithmic strainn 0 < e < 1...3. Methodology. The theoretical analysis of the regularities of deformation hardening of metals (alloys) from the engineering strain is carried out, the transition from engineering to logarithmic ("true") strain of metals (alloys) by analytical representation of metal hardening graphs as a function of logarithmic (true) strain. in contrast to the degree of engineering strain is presented. Originality. Analytical expressions are presented that allow the use of known theoretical data on the strain hardening of metals (alloys) at small (50...60 %) total engineering strains g during cold pressure treatment to transition to logarithmic (true) strain e with large total deformations. Practical value. The obtained mathematical expressions allow to use the accumulated in the technical literature experimental data on the hardening of metals and alloys with small engineering strains in the processes of cold processing of metals (alloys) by pressure to determine the hardening with large total logarithmic (true) strains. These data can also be used to solve metallophysical problems of metal processing by pressure associated with large total compressions.
 Keywords: cold forming of metals and alloys; hardening; degree of deformation

Effects of different alveolar bone finite element models on the biomechanical responses of periodontal ligament

In the study of oral orthodontics, the dental tissue models play an important role in finite element analysis results. Currently, the commonly used alveolar bone models mainly have two kinds: the uniform and the non-uniform models. The material of the uniform model was defined with the whole alveolar bone, and each mesh element has a uniform mechanical property. While the material of the elements in non-uniform model was differently determined by the Hounsfield unit (HU) value of computed tomography (CT) images where the element was located. To investigate the effects of different alveolar bone models on the biomechanical responses of periodontal ligament (PDL), a clinical patient was chosen as the research object, his mandibular canine, PDL and two kinds of alveolar bone models were constructed, and intrusive force of 1 N and moment of 2 Nmm were exerted on the canine along its root direction, respectively, which were used to analyze the hydrostatic stress and the maximal logarithmic principal strain of PDL under different loads. Research results indicated that the mechanical responses of PDL had been affected by alveolar bone models, no matter the canine translation or rotation. Compared to the uniform model, if the alveolar bone was defined as the non-uniform model, the maximal stress and strain of PDL were decreased by 13.13% and 35.57%, respectively, when the canine translation along its root direction; while the maximal stress and strain of PDL were decreased by 19.55% and 35.64%, respectively, when the canine rotation along its root direction. The uniform alveolar bone model will induce orthodontists to choose a smaller orthodontic force. The non-uniform alveolar bone model can better reflect the differences of bone characteristics in the real alveolar bone, and more conducive to obtain accurate analysis results.

Mapping and classifying large deformation from digital imagery: application to analogue models of lithosphere deformation

SUMMARY Particle image velocimetry (PIV), a method based on image cross-correlation, is widely used for obtaining velocity fields from time-series of images of deforming objects. Rather than instantaneous velocities, we are interested in reconstructing cumulative deformation, and use PIV-derived incremental displacements for this purpose. Our focus is on analogue models of tectonic processes, which can accumulate large deformation. Importantly, PIV provides incremental displacements during analogue model evolution in a spatial reference (Eulerian) frame, without the need for explicit markers in a model. We integrate the displacements in a material reference (Lagrangian) frame, such that displacements can be integrated to track the spatial accumulative deformation field as a function of time. To describe cumulative, finite deformation, various strain tensors have been developed, and we discuss what strain measure best describes large shape changes, as standard infinitesimal strain tensors no longer apply for large deformation. PIV or comparable techniques have become a common method to determine strain in analogue models. However, the qualitative interpretation of observed strain has remained problematic for complex settings. Hence, PIV-derived displacements have not been fully exploited before, as methods to qualitatively characterize cumulative, large strain have been lacking. Notably, in tectonic settings, different types of deformation—extension, shortening, strike-slip—can be superimposed. We demonstrate that when shape changes are described in terms of Hencky strains, a logarithmic strain measure, finite deformation can be qualitatively described based on the relative magnitude of the two principal Hencky strains. Thereby, our method introduces a physically meaningful classification of large 2-D strains. We show that our strain type classification method allows for accurate mapping of tectonic structures in analogue models of lithospheric deformation, and complements visual inspection of fault geometries. Our method can easily discern complex strike-slip shear zones, thrust faults and extensional structures and its evolution in time. Our newly developed software to compute deformation is freely available and can be used to post-process incremental displacements from PIV or similar autocorrelation methods.

Dynamic analysis of failure paths of truss structures: Benchmark examples including material degradation

We propose novel benchmark examples of dynamic failure paths of truss structures. Novelty arises from use of a logarithmic strain measure, within a total Lagrangian formulation, combined with a continuum material damage model. Previous benchmarks have considered the usual engineering strain measure, which is not always useful, as it can lead to material degeneration under finite levels of stress. Ductile material behavior has been considered in the literature, addressing plasticity and some material softening, but neglecting material degradation. Herein, damage accumulation is associated to the hydrostatic component of plastic strains, leading to a stable and explicit representation of material degradation. The original static formulation, presented elsewhere by the authors, is extended herein to the dynamic analysis of failure paths of truss structures. Several numerical examples from the literature are studied, and the differences in dynamic behavior are pointed out. In our implementation, as individual bars are damaged, elastic unloading and load redistribution are observed. When the critical damage hypothesized by Lemaitre is reached by individual bars, these are fully unloaded, with no material degeneration or numerical instability. Numerical results highlight the significant effects of material degradation in the dynamic behavior of truss structures under exceptional loads. We propose the set of examples addressed herein as the new benchmarks to which future developments in geometrical and material non-linear truss modelling will be compared.

Twinning and dynamic recrystallization of Mg–7Sn–3Zn alloy under high strain rate hot compression

Abstract In this study, we investigate the twinning behavior and dynamic recrystallization (DRX) of Mg–7Sn–3Zn alloy under a high strain rate (10 s−1) during hot compression deformation. At a relatively low temperature (300 °C) and high strain rate (10 s−1), the preferential occurrence of multiple { 10 1 ‾ 2 } 10 1 ‾ 1 > tension twin variant at the initial compressed stage is attributed to the Schmid factor (SF) criterion, and the following { 10 1 ‾ 2 } 10 1 ‾ 1 > tension twin variants nucleate because of the geometric compatibility factor mʹ of the ortho-position twin pair. Because of the growth and interaction between the ortho-position { 10 1 ‾ 2 } 10 1 ‾ 1 > tension twin pairs, the volume fraction of 60° 10 1 ‾ 0 > boundaries evidently increases. Moreover, as the logarithmic strain increases, the volume fraction of { 10 1 ‾ 2 } 10 1 ‾ 1 > tension twins and 60° 10 1 ‾ 0 > boundaries significantly decreases, and a few { 10 1 ‾ 1 } 10 1 ‾ 2 > compression twins and { 10 1 ‾ 2 }–{ 10 1 ‾ 1 } double twins form. Then, twinning-induced dynamic recrystallization (TDRX) as a primary DRX mechanism occurs in { 10 1 ‾ 1 } 10 1 ‾ 2 > compression twins and { 10 1 ‾ 2 }–{ 10 1 ‾ 1 } double twins. These results indicate that at a high temperature (400 °C) and 10 s−1, certain { 10 1 ‾ 2 } 10 1 ‾ 1 > tension twins form during the early stage compression in accordance with the SF criterion, and discontinuous DRX (DDRX) occurs along the original grain boundaries because of the higher deformation temperature, which increases the nucleation rate and promotes the migration of grain boundaries. With the accumulation of logarithmic strain, continuous DRX (CDRX) occurs. The recrystallization grains consume the twin boundaries, which causes the { 10 1 ‾ 2 } 10 1 ‾ 1 > tension twins to merge. Under the same logarithmic strain, when the deformation temperature increases from 300 °C to 400 °C, the DRX process is significantly improved.

A finite strain thermomechanically-coupled constitutive model for phase transformation and (transformation-induced) plastic deformation in NiTi single crystals

A 3D finite-strain constitutive model for the deformation response of NiTi at the single crystal level is proposed. The model accounts for reversible phase transformation from austenite to martensite habit plane variants, plastic deformation in the austenite phase, and rate effects induced from latent heat. It is developed within the formalism of irreversible thermodynamics with internal state variables based on the Eulerian logarithmic strain and its corrotational objective rate. The inelastic deformation is defined as an average over a representative volume element as classical in the micromechanics-based modeling approach. Transformation-induced plastic deformation is viewed as a mechanism for accommodation of the local deformation incompatibility at the austenite–martensite interface. It is accounted for by introducing an interaction term in the free energy, which is described through the Eshelby tensor by regarding the habit plane variants as ellipsoidal inclusions embedded in the austenite matrix, in order to accurately reflect the internal stress states that contribute to dislocation slipping. The numerical implementation of the model in an efficient scheme and its calibration are described in detail. The proposed model is validated by comparing simulations with available experimental data in single NiTi crystals. Numerical simulations of polycrystals are performed to obtain an insight into the interaction between phase transformation and plastic deformation induced by intergrannular constraints. The efficiency of the numerical implementation of the model is verified by simulations of indentation tests.

A finite strain solution for strain-softening rock mass around circular roadways

This paper presents a semi-analytical finite strain solution for circular roadways excavated in a strain-softening rock mass with a non-associated flow rule. The evolutions of both strength parameters and Young’s modulus are considered, and the finite strains are applied to describe both the elastic and plastic behaviors with the logarithmic strain in Lagrangian coordinates. By transforming the derivative of displacement with a new variable that is correlated with displacement, the stress and displacement in the elastic region are obtained in the form of integral equations. Considering the assumption of constant material parameters within a very small region, the plastic region is divided into a number of concentric annuli, whose closed-form solutions of displacement and stress can be recursively obtained. The solution is validated by similarity solutions and numerical simulation. Both the roadway wall displacement and thickness of the plastic (residual) region appear to be smaller than those of the small strain solution. For the elasto-perfectly-plastic rock mass, the finite strain solution is approximately the same as that of small strain solution. However, for the strain-softening rock mass, with the decrease of Young’s modulus, the thickness of plastic and residual regions shows the first increase and then decrease trend, finally approaching nil; the difference between the thickness of softening and residual region gradually decreases. The decreasing Young’s modulus deterioration coefficient and increasing dilation angle significantly produce the displacement. Both the displacement and the thickness of plastic and residual regions decrease with the increase of Poisson’s ratio. When Young’s modulus is large, the tangential stress gradually decreases with the increasing radius. When Young’s modulus is small, the tangential stress firstly increases to a maximum value, then decreases gradually. Different from the small strain solutions, the roadway wall displacement of finite strain solutions cannot be larger than the excavation radius, which is in compliance with the practical underground engineering condition. The predicted displacement and thickness in both plastic and residual regions are in accordance with the field test results.

Characterization on the formation of porosity and tensile properties prediction in die casting Mg alloys

The 3D visualization of the porosity in high-pressure die casting (HPDC) Mg alloys AZ91D and Mg4Ce2Al0.5Mn (EA42) was investigated by X-ray computed tomography. It was demonstrated that the volumetric porosity at the near-gate location for alloy EA42 was significantly higher than that far from the gate location. This difference resulted from the low valid time during intensified casting pressure conditions. Specimens of alloy EA42 exhibited a narrow pore distribution in the side view (∼0.5 mm) compared to the wide distribution (∼1.8 mm) of alloy AZ91D, which was mainly attributed to the formation mechanism of the defect band. The formation of microporosity in the defect band of alloy EA42 was inhibited because of the significant latent heat released by a large amount of the Al11Ce3 phase segregated in the defect band during solidification. Additionally, an effective estimator (Z-Propagation) was introduced, which is proposed to predict the projected area fraction of the porosity (f) involved during tensile failure with better effectiveness compared with traditional methods based on the actual fractured surface. By coupling the Z-Propagation method with the critical local strain model, the logarithmic fracture strain and true fracture stress of the specimens were predicted within 3.03% and 1.65% of the absolute value of the average relative error (AARE), respectively.

Physical simulation of hot rolling of powder metallurgy-based Al/SiC composite by plane strain multi stage compression

The development of lightweight materials like Al/SiC metal matrix composite sheet is a challenge by different manufacturing processes for further application in the automobile and aerospace industries. In the present work, plane strain multistage compression was used to investigate the hot rolling of powder metallurgy-based Al/7vol.%SiC composite. The cuboids of dimension (80 mm × 45 mm × 15 mm) from this composite material were synthesized using a conventional powder metallurgy technique. Then, the plane strain samples were cut from these composite cuboids. After that, plane strain multistage compression tests were performed using a thermo-mechanical simulator, Gleeble-3800. The multistage compression consists of six stages of different strains and all stages were compressed at a constant strain rate (1 s−1) to achieve a final logarithmic strain of 1.5. All the plane strain stages were conducted at four different temperatures (350, 400, 450 and 500 °C). The flow curves obtained from the plane strain experiments show the initial hardening, then steady-state followed by final hardening. A constitutive equation for flow stresses has been developed and it predicts within the error of 2.62–6.18%. Then, the activation energy and dislocation densities are calculated and analyzed. Dislocation density is significantly high for this composite at the end of deformation as compared to the sintered one. After that, hot rolling experiments were conducted to make the Al/7vol.%SiC composite sheets. A comparative microstructural characterization has been examined using the optical image and electron backscatter diffraction. Recrystallized, deformed and sub-structured grains were observed in the hot-rolled sheet. The tensile fracture mechanisms are particle crack, void, growth and facet, whereas the edge crack in the plane strain samples due to particle crack and debonding. This study opens up the possible use of plane strain compression to design the hot rolling process in the industry for Al-metal matrix composites sheets.

A two-parameter strain energy function for brain matter: An extension of the Hencky model to incorporate locking

By just replacing the infinitesimal strains by logarithmic strains, the Hencky strain energy has proven to extend successfully the infinitesimal framework to moderately large strains, as those found in brain. However, as polymers and soft tissues, brain presents an important strain-stiffening towards locking. Based on both observations, in this paper we propose a simple two-parameter isotropic strain energy function for representing the inviscid (conservative) behavior of brain matter. The two parameters of the model are the Young modulus (or alternatively the shear modulus) and the locking stretch during a test. Through a comparison with experimental data, we show that with this simple model, employing the two material parameters directly measured from a tensile test, we capture the qualitative aspects and quantitative behavior of brain mater in tension, compression and simple shear tests with good accuracy. Statement of SignificanceThis paper shows a simple mathematical model capable of reproducing qualitative aspects and quantitative behavior of brain matter in tension, compression and simple shear tests with good accuracy. The model is governed by only two parameters, namely Young's modulus (or alternatively the shear modulus) and the locking stretch.

Measurement and Analysis of Deformation Behavior of Polyethylene Tube Subjected to Biaxial Tensile Stress with Large Strain

A material testing apparatus for measuring the biaxial deformation behavior of a polymer tube is developed to quantitatively evaluate the deformation behavior of polymeric materials. The testing apparatus can apply axial force and internal pressure to a tubular specimen. A noncontact strain measurement system is also developed, and the biaxial strain components and the radius of curvature in the axial direction of the specimen are continuously measured to control the stress path applied to the specimen. Polyethylene tubes with an outer diameter of 17 mm and a thickness of 2 mm are used as test specimens, that are subjected to linear stress paths with stress ratios of σφ :σθ =1:0, 4:1, 2:1, 4:3, 1:1, 3:4, 1:2, 1:4, and 0:1, where σφ and σθ are the axial and circumferential stress components applied to the center of the bulging specimen, respectively. Biaxial stress-strain curves are successfully measured for every linear stress path at a nearly constant logarithmic strain rate of 1×10-3 s-1. A maximum equivalent strain of up to 0.71 is achieved for a specimen with a stress path of σφ :σθ =2:1. The contours of equal work plotted in the principal stress space show a significant anisotropy of the test material.