Effect Of Strain History Research Articles

A new multiaxial loading test for investigating the mechanical behaviour of polymers

In order to investigate polymer mechanical behaviour more closely and define corresponding numerical behaviour models, a new experimental set-up was developed for performing multiaxial loading tests. Some of the loading possibilities are presented here for the case of a copolymer polypropylene (PPC7712). A single moulded sample of this material was mounted on this original apparatus, which was specially designed for studying complex trajectories, including proportional and non-proportional cycles, in which the axial and shear deformation can be simultaneously and independently controlled. Tension/compression/torsion tests were performed on the polypropylene material, spanning all four quadrants of the axial/torsional strain subspace. Under the conditions tested, the effect of strain history on the stress-strain response is hardly observed for this material. The qualitatively different behaviour observed depending on the strain path might be attributable to the asymmetry between the axial/torsional and tension/compression loads.

Surface topography changes in aluminum alloy sheet during large plastic straining under cyclic pure bending

This study consists of the experimental assessment of the surface topography of aluminum alloy AA 6022 sheet during large cyclic tensile and compressive plastic straining such as those present in the flow through drawbeads and small corner radii. Uniaxial and cyclic bending tests were used to measure the effects of such strains on the substrate layers of the sheet. All testing was performed without tool contact to ensure surface roughness changes were exclusively the result of the straining evolution of the free outer layers. The three-dimensional average surface roughness (Sa) was measured using optical interferometry. Changes in Sa were evaluated for two sheet textures: mill finish (MF) and electro discharge texture (EDT), along longitudinal and transverse rolling directions. Texture pattern, test direction, and bending/unbending strain are all shown to be significant contributors to variations in Sa. The magnitude of the initial surface roughness was also an important factor of the resultant %Sa variation, ranging from 40% ΔSa for EDT, to approximately 350% ΔSa for MF. Unbending the sample to its flat state considerably altered the Sa, disturbing any monotonic Sa trend. This made it unfeasible to assess the effects of strain history on a formed part based only on Sa values. The non-linear relationship between Sa and strain was more significant at medium and large strains. Effects on Sa due to bending/unbending of the substrate layer presented in this study must be taken into account in the modeling of more complex phenomena involving tool radii contact and friction.

ゴムのシミュレーション技術 ゴム応力軟化シミュレーション技術の最新動向

Many rubber-like materials consist of a cross-linked elastomeric substance with a dispersed small carbon particles as fillers. A piece of filler loaded rubber subjected to a series of loadings typically displays pronounced stress softening associated with damage. This stress softening phenomenon is referred to as the Mullins effect. The effects of strain history on the stresses and the formulation of constitutive models for filled and unfilled elastomers have been a particular focus of attention during the last few years. In this general remark, some representative damage functions are explicated through general purpose FEM programs. Furthermore, the anisotropic Mullins effect is indicated by biaxial experimental cyclic test. The numerical model of anisotropic Mullins effect, eventually, is expounded, and its numerical analysis is illustrated by using user-subroutine on Marc.

Mobilisation of Earth Pressure Acting on Pile Caps Under Cyclic Loading

ABSTRACT In lateral resistance of piles with a pile cap, marked contribution of the pile cap resistance can be expected. For seismic performance assessment of pile foundations, mobilisation of the earth pressure acting on pile caps, induced by interactions between the pile cap and surrounding soils, has to be properly considered. In this study, a series of centrifuge model tests were conducted (1) to examine the effect of strain history on the mobilization of lateral earth pressure acting on pile caps and (2) to show the importance of considering strain history when modelling the interaction between a surface soil layer and a pile cap. Observations into the physical model tests reveal that mobilisation of the earth pressure acting on pile caps under cyclic loading can drastically change depending on soil type and/or conditions. Especially, relocation of soil adjacent to the pile cap in unload-reload phase plays an important role for the earth pressure mobilisation, as it completely alters the shape of the earth pressure-displacement curves. Based on the physical model test results, a simple empirical model that can be used for the beam on non-linear Winkler foundation type analysis is proposed and compared to the test results.

Inelastic constitutive relations for foamed materials: A statistical approach and its application to open-cell melamine

The aim of this study is to characterize the viscoelastic behavior at finite strain of a melamine foam submitted to multiple loading paths of uniaxial compression. The constitutive law is obtained by specializing a previously proposed model arising from an irreversible thermodynamic approach for several types of material (e.g. polymer, metal alloys) to include the essential microscopic features of this open-cell foam. The model is based on the central concept of relaxed state, which is defined as a thermodynamic state of metastable equilibrium including the strain history effect. In the case of the present material, it is shown that the corresponding relaxed stress may thus be formulated using the tools of statistical mechanics: namely, the Shannon entropy 〈 S〉 is extremized under adequate geometric constraints. Thus, the Lagrange multipliers associated with these requirements are defined as forces conjugated to the degrees of freedom of the geometrical transformation. By comparing the predictions from the proposed inelastic constitutive model with experimental data for uniaxial compression interrupted by loading–unloading sequences, we conclude that the constitutive relations predict the mechanical behavior of the melamine foam.

Numerical Solution Methods for the Elastomeric Damage Model

Many rubber-like materials consist of a cross-linked elastomers substance with a distribution of small carbon particles as fillers. A piece of filler loaded rubber subjected to a series of loadings typically displays pronounced stress softening associated with damage. This stress softening phenomenon is referred to as the Mullins effect. The effects of strain history on the stresses and the formulation of constitutive models for filled and unfilled elastomers have been a particular focus of attention during the last few years. In this general remark, some representative damage functions are compared and two examples of permanent set are showed with maximal use of user-subroutine.

Effect of Strain History on Stress and Permanent Set in Cross-Linking Networks: A Molecular Dynamics Study

Polymer networks undergoing cross-linking reactions are studied using molecular dynamics simulations to investigate how the stress is influenced by the coupling between cross-linking and deformation. For networks cross-linked in the undeformed state, the modulus increases linearly with the cross-link density as expected from rubber elasticity theory. When cross-links are added to a network that was uniaxially deformed, the stress remains constant in accordance with the independent network hypothesis of Tobolsky. When the deformed network is subsequently released, permanent set is observed. Using the independent network hypothesis, together with the affine theory of rubber elasticity, a constitutive model is developed that accounts for the effect of the coupling between the cross-link density and strain histories of the network. The permanent set predictions from the affine model are higher than found from MD simulations.

A dislocation-based analysis of strain history effects in ice

Abstract The cyclic loading response of ice specimens can be analysed with a dislocation-based model of anelasticity to produce an estimate of the effective mobile dislocation density. Moreover, the cyclic loading response is sufficiently sensitive to track the dislocation density changes that occur during creep straining. A combination of cyclic and creep loading experiments can thus be employed to gain crucial insight regarding the relationship between the dislocation density that evolves during creep straining and the anelastic and viscous components of strain. Creep and cyclic loading experiments have been conducted on laboratory-prepared saline and freshwater ice specimens to shed light on the effects of temperature, creep stress and accumulated strain on the mobile dislocation density and thereby to support the further development of a physically based constitutive model for ice. The findings indicate that, in addition to the expected stress and strain dependence, the dislocation density that develops during straining also depends on the temperature and microstructure. As a consequence of this temperature dependence, the apparent activation energy for creep when dislocation multiplication takes place is higher than that for creep in the absence of dislocation multiplication. Data from the literature are examined and found to support this finding. The results indicate that both the anelastic strain and the viscous strain rate vary with the mobile dislocation density. A preliminary set of results indicates that the power law stress exponent n is 3 when the applied stress is high enough to cause an increase in the dislocation density, but that n ≈ 1 when the dislocation density remains constant during straining. The results show that prior straining increases the stress level associated with the transition from n = 1 to n = 3. The findings provide support for the glide-controlled mechanism of ice creep, and a dislocation glide-based formulation for viscous straining is presented. The model agrees well with the experimental data in the pure flow regime.

A dislocation-based analysis of strain history effects in ice

Abstract The cyclic loading response of ice specimens can be analysed with a dislocation-based model of anelasticity to produce an estimate of the effective mobile dislocation density. Moreover, the cyclic loading response is sufficiently sensitive to track the dislocation density changes that occur during creep straining. A combination of cyclic and creep loading experiments can thus be employed to gain crucial insight regarding the relationship between the dislocation density that evolves during creep straining and the anelastic and viscous components of strain. Creep and cyclic loading experiments have been conducted on laboratory-prepared saline and freshwater ice specimens to shed light on the effects of temperature, creep stress and accumulated strain on the mobile dislocation density and thereby to support the further development of a physically based constitutive model for ice. The findings indicate that, in addition to the expected stress and strain dependence, the dislocation density that develo...

Micromechanics of cyclic softening in thermoplastic vulcanizates

The strain history dependence of the stress–strain behavior of thermoplastic vulcanizate (TPV) materials is studied through a set of experiments and micromechanical models. Thermoplastic vulcanizates are a class of composite material consisting of a high volume fraction of fully-cured elastomeric particles in a thermoplastic matrix. The stress–strain behavior of TPVs is found to soften after having been subjected to an initial load/unload cycle. In this paper, the TPV strain history dependence is experimentally documented on a representative TPV material (TPV-R) by subjecting TPV-R to load/unload/reload histories in plane strain compression to various magnitudes of strain. The stress–strain behavior is observed to be more compliant upon reloading, but the tangent modulus is found to increase with strain until the reloading stress–strain curve joins the initial curve. An increase in the magnitude of the initial strain excursion increases the compliance observed during reloading. The unloading behavior following the reload is very similar to the unloading behavior following the initial load. The underlying microscopic mechanisms which govern the strain history effects are investigated using micromechanical modelling of the composite structure and its deformation. The stress–strain behaviors predicted by the simulations are found to be in good agreement with the experimentally observed behavior over the entire strain history for each magnitude of strain considered. The models reveal the softening of the material to result from a reorganization of the particle/matrix microstructural configuration due to plastic stretching of interparticle ligaments during the initial load step followed by ligament bending and rotation during the unloading step. The new microstructural configuration that exists after the first load/unload cycle favors bending and rotation of the (now thinned) matrix ligaments (as opposed to plastic deformation of the ligaments) during reloading; the ligament bending and rotation occur under low stress levels which results in the more compliant response. The additional features of the stress–strain behavior during reloading are also captured well by the model.

Evaluation of Gravel Stiffness by Pulse Wave Transmission Tests

Abstract Laboratory techniques for the measurements of very small strain stiffness parameters of coarse-grained materials include: (a) static tests using local strain transducers like LDTs and (b) wave propagation measurements performed using bender elements, shear plates, and so on. The former method has been employed for most kinds of soil, while the use of wave propagation methods has been restricted to small specimens of sand and clay. At the University of Naples Federico II (DIG), a simple device to generate and monitor compressional and shear waves has been designed to be used in large-scale triaxial apparatuses. The testing device was first used on densely compacted gravel specimens in a large triaxial apparatus in Naples and, after some further improvements, also in another large triaxial cell in Tokyo. In the tests carried out in Tokyo, dynamic and static measurements were performed simultaneously on the single gravel specimens. In this paper, the details of the new system are presented and the results are discussed. The comparison between stiffness moduli evaluated by dynamic and static measurements shows that density, stress state, and strain history effects are similar, but that the dynamically measured stiffness values are consistently larger, about two times, than the statistically determined ones. Since the stiffness of gravels has proven to be strain rate independent, possible reasons for this difference are addressed.

Impact compression behavior of FCC metals with pre-torsion strains

This paper investigates the effect of non-proportional pre-straining path on flow behavior of FCC metals at impact compression, where reversed torsion strain is introduced following 10% pre-torsion. Two kinds of FCC metals, Al and Cu, are employed to also examine the material dependency. Experimental results demonstrate that significant interaction exists between strain history and strain rate effects, which is strongly material dependent. The reversed torsion temporarily reduces strain history effect for Al. The trend is shown to be described qualitatively by analysis based on the crystalline plasticity theory where newly proposed back stress model considering piling-up behavior of dislocations is introduced.

衝撃 ＦＣＣ金属の衝撃圧縮挙動に及ぼすねじり予ひずみの影響

This paper systematically studies the effect of nonproportional strain history on the flow behavior of FCC metals at high strain rates. Impact compression tests with pre-torsion strain ranging from 0% to 10% are performed at several rates up to 103s-1 by using a split Hopkinson pressure bar method. Two kinds of materials with different stacking fault energy, i.e., pure aluminum and pure copper, are employed to examine also the material dependency. The experimental results demonstrate that there exsts significant interaction between strain history and strain rate effect, which is strongly material dependent. The strain history effect tends to disappear at high strain rates for pure Al, whereas it becomes large under impact loading for Cu. The controlling micromechanism which describes both the above positive and negative interactions is extensively, discussed based on dislocation interaction. The effect of prestraining path is also discussed, where reversed torsion is introduced following 10% pre-torsion. The reversed pre-torsion straining tentatively reduces the strain history effect for Al, while no reduction in flow stress is observed in Cu. These trends are found to become strong for both the materials as the strain rate increases.

Constrained Densification of Alumina/Zirconia Hybrid Laminates, II: Viscoelastic Stress Computation

To analyze the inhibited densification during sintering and differential shrinkage during cooling of Al2O3/ZrO2symmetric and asymmetric laminates, viscoelastic formulations, in which the viscosity and elastic modulus vary with time, have been developed. The viscoelastic mismatch stresses have been numerically computed over the entire processing cycle, including the heating period, the isothermal period, and the cooling period. The viscosity and free sintering rates that are needed for stress computation have been obtained by modifying the parameters that are measured for a normal isotropic densifying compact using cyclic loading dilatometry. The modification is based on the available sintering models to account for the effect of strain history on compact viscosity and sintering rates. The stress calculation shows that, with the exception of the initial heating period, the viscoelastic stress is identical to the viscous stress that is calculated solely from the strain rate mismatch. Sintering damage in the laminates is shown to occur during densification under conditions where the differential sintering stress is smaller than the intrinsic sintering pressure. The magnitude of residual stress in hybrid laminates on cooling is dependent on the cooling rate, and slower cooling rates are capable of almost completely relaxing the expansion mismatch stress at temperatures of >1200°C.

Cyclic Stress-Strain Curves of Polyoximethylene under Combined Tension-Torsion.

In order to construct a constitutive equation for polymeric solids, cyclic combined tension-torsion tests were performed using polyoximethylene (POM) at strain paths such as proportional, cruciform, rhombus and circular ones to investigate the effect of strain history on the stress-strain curve. It was shown that : (1) cyclic softening occurs for all strain paths tested here, (2) stress response for all strain paths is influenced by the hydrostatic stress component, (3) stress softening for the circular strain path greatly depends on the previous strain path and (4) stress relaxation after several stroain cycles strongly depends on the direction of the present strain.

Influence of time‐temperature history and strain history on the melt rheology of soy protein isolate at an elevated temperature

Summary.Reciprocating extrusion and single extrusion experiments were performed using a completely air‐tight capillary extrusion viscometer in order to elucidate the effects of time‐temperature history and strain history on the melt rheology of soy protein isolate (SPI) at an elevated temperature (140°C). Both histories produced a decrease in the measured pressure drop during extrusion and these effects were strongly dependent on the sample moisture content. For moisture contents above 41% (dry basis), the time‐temperature history effect was predominant more in decreasing the measured pressure drop, whereas the strain history effect was more influential at moisture contents below 30% (d.b.)

結晶性高分子材料の繰返しねじり応力・ひずみ曲線に及ぼすひずみ履歴と圧力の影響

In order to investigate a nonlinear constitutive equation of polymers at finite strain for polymer solids, tension, torsion and combined tension-torsion tests under constant strain rate, stress relaxation and creep have been conducted to provide experimental data required for constructing the equation. Although the stress response under strain paths with its reversal is very important to understand fatigue behavior, there has been few experiments for polymers. Hence, the effect of strain history on the constitutive equation still remains unclear. Furthermore. the constitutive equation still remains unclear. Furthermore, the pressure dependent behavior on the exact stress-strain curves has not been observed in spite of many experiments on the pressure dependence of elastic modulus and flow stress. In this paper, cyclic torsional tests under hydrostatic pressures of 1 to 2000kgf/cm2 were carried out to describe both pressure and cyclic dependent behavior for crystalline polymers of polyethylene (PE), polypropylene (PP) and polyoximethylene (POM). It has been shown that (1) the shape of the stress-strain curves is not significantly affected by applied pressures, (2) cyclic softening occurs for the materials tested, but the degree of softening is dependent on materials, (3) the stress responses under partly reversed cyclic loading are differnt from the ones expected from fully reversed cyclic loading and (4) the stress responses for POM and PP are very sensitive to strain history, while the current stress-strain curve for PE is little affected by the previous strain paths.

Stress-strain behaviour at finite strains for various strain paths in polyethylene

In order to provide new experimental facts required for constructing a non-linear constitutive equation for crystalline polymers, some tests were conducted by the use of polyethylene (PE) under various strain histories such as tension, torsion, tension-torsion proportional strain path, tension-torsion cruciform strain path, tension-torsion circular strain path, and various cyclic loadings. It is shown that (i) since the stress-strain behaviour for PE is not very sensitive to hydrostatic pressure, the equivalent stress and strain of von Mises type are useful for its description; (ii) the stress range at a constant strain amplitude at partly reversed cyclic loading tends to increase with an increase in the number of cycles, but the stress amplitude at fully reversed cyclic loading is nearly independent of the number of cycles; (iii) the degree of cyclic softening or hardening is relatively small compared with that of polypropylene; and (iv) under the conditions tested here, the effect of strain history on the stress-strain response is hardly observed for PE.

Effects of strain history on the damage accumulation rate in nonmonotone elastoplastic loading

Effects of strain history on the damage accumulation rate in nonmonotone elastoplastic loading

Strain history effects at low temperature deformation

AbstractThe work hardening coefficient of hep metals like Zn or Cd depends on the temperature even at very low temperatures. Additional information of the processes involved can be derived from specially designed annealing experiments. If deformed single crystals of Zn, Zn + 0.2 at.% Ga and Zn + 0.2 at.% Ag are annealed the work hardening increases. The amount of increase depends on deformation temperature and annealing time. The effects observed suggest that the work hardening is determined at least partly by the mobility of points defects.