Residual properties of an injection-molded poly(phenylene ether ketone) carbon composite during flexural fatigue

The present work investigates the effects of cyclic fatigue loading on the residual properties of an injection-molded composite, carbon-fiber-reinforced poly(phenylene ether ketone) (CF/PEK-C), and damage development in this material under fatigue lending. Test specimens, which had been conditioned to various preselected fatigue damage stages, were measured for their residual properties. The results indicated that cyclic fatigue loading alters the constitutive behavior of the injection-molded composite, especially in the non-linear portion of the stress/strain curve. The residual strength decreases with increase in the number of fatigue cycles as a consequence of the accumulation of fatigue damage, which is dominated by the growth of microcracks. While the residual modulus increases slightly with cyclic fatigue loading, this is probably due to the oriented hardening resulting from creep deformation which is induced during cyclic loading. (C) 1997 Elsevier Science Limited.

Hyperelastic constitutive relationship for the strain-rate dependent behavior of shoulder and other joint cartilages

Non-linear finite deformations of articular cartilages under physiological loading conditions can be attributed to hyperelastic behavior. This paper contains experimental results of indentation tests in finite deformation and proposes an empirical based new generalized hyperelastic constitutive model to account for strain-rate dependency for humeral head cartilage tissues. The generalized model is based on existing hyperelastic constitutive relationships that are extensively used to represent biological tissues in biomechanical literature. The experimental results were obtained for three loading velocities, corresponding to low (1x10-3 s-1), moderate and high strain-rates (1x10-1 s-1), which represent physiological loading rates that are experienced in daily activities such as lifting, holding objects and sporting activities. Hyperelastic material parameters were identified by non linear curve fitting procedure. Analysis demonstrated that the material behavior of cartilage can be effectively decoupled into strain-rate independent(elastic) and dependent parts. Further, experiments conducted using different indenters indicated that the parameters obtained are significantly affected by the indenter size, potentially due to structural inhomogeneity of the tissue. The hyperelastic constitutive model developed in this paper opens a new avenue for the exploration of material properties of cartilage tissues.

Constitutive equation for elevated temperature flow behavior of plain carbon steels using dimensional analysis

Dimensional analysis using π-theorem is applied to the variables associated with plastic deformation. The dimensionless groups thus obtained are then related and rewritten to obtain the constitutive equation. The constants in the constitutive equation are obtained using published flow stress data for carbon steels. The validity of the constitutive equation is tested for steels with up to 1.54 wt%C at temperatures: 850–1200 °C and strain rates: 6 × 10−6–2 × 10−2 s−1. The calculated flow stress agrees favorably with experimental data.

A constitutive model for the in-plane mechanical behavior of nonwoven fabrics

A constitutive model is presented for the in-plane mechanical behavior of nonwoven fabrics. The model is developed within the context of the finite element method and provides the constitutive response for a mesodomain of the fabric corresponding to the area associated to a finite element. The model is built upon the ensemble of three blocks, namely fabric, fibers and damage. The continuum tensorial formulation of the fabric response rigorously takes into account the effect of fiber rotation for large strains and includes the nonlinear fiber behavior. In addition, the various damage mechanisms experimentally observed (bond and fiber fracture, interfiber friction and fiber pull-out) are included in a phenomenological way and the random nature of these materials is also taken into account by means of a Monte Carlo lottery to determine the damage thresholds. The model results are validated with recent experimental results on the tensile response of smooth and notched specimens of a polypropylene nonwoven fabric.

A multiscale multisurface constitutive model for the thermo-plastic behavior of polyethylene

We present a multiscale model bridging length and time scales from molecular to continuum levels with the objective of predicting the yield behavior of amorphous glassy polyethylene (PE). Constitutive pa- rameters are obtained from molecular dynamics (MD) simulations, decreasing the requirement for ad- hoc experiments. Consequently, we achieve: (1) the identification of multisurface yield functions; (2) the high strain rate involved in MD simulations is upscaled to continuum via quasi-static simulations. Validation demonstrates that the entire multisurface yield functions can be scaled to quasi-static rates where the yield stresses are possibly predicted by a proposed scaling law; (3) a hierarchical multiscale model is constructed to predict temperature and strain rate dependent yield strength of the PE.

Effect of constitutive material models on seismic response of two-story reinforced concrete frame

This paper focuses on the finite element (FE) response sensitivity and reliability analyses considering smooth constitutive material models. A reinforced concrete frame is modeled for FE sensitivity analysis followed by direct differentiation method under both static and dynamic load cases. Later, the reliability analysis is performed to predict the seismic behavior of the frame. Displacement sensitivity discontinuities are observed along the pseudo-time axis using non-smooth concrete and reinforcing steel model under quasi-static loading. However, the smooth materials show continuity in response sensitivity at elastic to plastic transition points. The normalized sensitivity results are also used to measure the relative importance of the material parameters on the structural responses. In FE reliability analysis, the influence of smoothness behavior of reinforcing steel is carefully noticed. More efficient and reasonable reliability estimation can be achieved by using smooth material model compare with bilinear material constitutive model.

Ratcheting and wear behavior of Australian rail steel: Experimental investigation of material properties and sampling method

To The ratcheting behavior of high-strength rail steel (Australian Standard AS1085.1) is studied in this work for the purpose of predicting wear and damage to the rail surface. Historically, researchers have used circular test coupons obtained from the rail head to conduct cyclic load tests, but according to hardness profile data, considerable variation exists across the rail head section. For example, the induction-hardened rail (AS1085.1) shows high hardness (400-430 HV100) up to four-millimeters into the rail head’s surface, but then drops considerably beyond that. Given that cyclic test coupons five millimeters in diameter at the gauge area are usually taken from the rail sample, there is a high probability that the original surface properties of the rail do not apply across the entire test coupon and, therefore, data representing only average material properties are obtained. In the literature, disks (47 mm in diameter) for a twin-disk rolling contact test machine have been obtained directly from the rail sample and used to validate rolling contact fatigue wear models. The question arises: How accurate are such predictions? In this research paper, the effect of rail sampling position on the ratcheting behavior of AS1085.1 rail steel was investigated using rectangular shaped specimens. Uniaxial stress-controlled tests were conducted with samples obtained at four different depths to observe the ratcheting behaviour of each. Micro-hardness measurements of the test coupons were carried out to obtain a constitutive relationship to predict the effect of depth on the ratcheting behaviour of the rail material. This work ultimately assists the selection of valid material parameters for constitutive models in the study of rail surface ratcheting.

Study on the elastic-plastic behavior of a porous hierarchical bioscaffold used for bone regeneration

A perfectly plastic von Mises model is proposed to study the elastic-plastic behavior of a porous hierarchical scaffold used for bone regeneration. The proposed constitutive model is implemented in a finite element (FE) routine to obtain the stress-strain relationship of a uniaxially loaded cube of the scaffold, whose constituent is considered to be composed of cortical bone. The results agree well with experimental data for uniaxial loading case of a cancellous bone. We find that the unhomogenized stress distribution results in different mechanical properties from but still comparable to our previous theory. The scaffold is a promising candidate for bone regeneration.

Modeling of dynamic material behavior in hot deformation: Forging of Ti-6242

A new method of modeling material behavior which accounts for the dynamic metallurgical processes occurring during hot deformation is presented. The approach in this method is to consider the workpiece as a dissipator of power in the total processing system and to evaluate the dissipated power co-contentJ = ∫o σ ε ⋅dσ from the constitutive equation relating the strain rate (ε) to the flow stress (σ). The optimum processing conditions of temperature and strain rate are those corresponding to the maximum or peak inJ. It is shown thatJ is related to the strain-rate sensitivity (m) of the material and reaches a maximum value(J max) whenm = 1. The efficiency of the power dissipation(J/J max) through metallurgical processes is shown to be an index of the dynamic behavior of the material and is useful in obtaining a unique combination of temperature and strain rate for processing and also in delineating the regions of internal fracture. In this method of modeling, noa priori knowledge or evaluation of the atomistic mechanisms is required, and the method is effective even when more than one dissipation process occurs, which is particularly advantageous in the hot processing of commercial alloys having complex microstructures. This method has been applied to modeling of the behavior of Ti-6242 during hot forging. The behavior of α+ β andβ preform microstructures has been exam-ined, and the results show that the optimum condition for hot forging of these preforms is obtained at 927 °C (1200 K) and a strain rate of 1CT•3 s•1. Variations in the efficiency of dissipation with temperature and strain rate are correlated with the dynamic microstructural changes occurring in the material.

Constitutive model for municipal solid waste incorporating mechanical creep and biodegradation-induced compression

A constitutive model is proposed to describe the stress-strain behavior of municipal solid waste (MSW) under loading using the critical state soil mechanics framework. The modified cam clay model is extended to incorporate the effects of mechanical creep and time dependent biodegradation to calculate total compression under loading. Model parameters are evaluated based on one-dimensional compression and triaxial consolidated undrained test series conducted on three types of MSW: (a) fresh MSW obtained from working phase of a landfill, (b) landfilled waste retrieved from a landfill after 1.5 years of degradation, and (c) synthetic MSW with controlled composition. The model captures the stress-strain and pore water pressure response of these three types of MSW adequately. The model is useful for assessing the deformation and stability of landfills and any post-closure development structures located on landfills.

On the mechanical behavior of compacted pack ice : A theoretical and numerical investigation

Pack ice is an aggregate of ice floes drifting on the sea surface. The forces controlling the motion and deformation of pack ice are air and water drag forces, sea surface tilt, Coriolis force and the internal force due to the interaction between ice floes. In this thesis, the mechanical behavior of compacted pack ice is investigated using theoretical and numerical methods, focusing on the three basic material properties: compressive strength, yield curve and flow rule. A high-resolution three-category sea ice model is applied to investigate the sea ice dynamics in two small basins, the whole Gulf Riga and the inside Pärnu Bay, focusing on the calibration of the compressive strength for thin ice. These two basins are on the scales of 100 km and 20 km, respectively, with typical ice thickness of 10-30 cm. The model is found capable of capturing the main characteristics of the ice dynamics. The compressive strength is calibrated to be about 30 kPa, consistent with the values from most large-scale sea ice dynamic studies. In addition, the numerical study in Pärnu Bay suggests that the shear strength drops significantly when the ice-floe size markedly decreases. A characteristic inversion method is developed to probe the yield curve of compacted pack ice. The basis of this method is the relationship between the intersection angle of linear kinematic features (LKFs) in sea ice and the slope of the yield curve. A summary of the observed LKFs shows that they can be basically divided into three groups: intersecting leads, uniaxial opening leads and uniaxial pressure ridges. Based on the available observed angles, the yield curve is determined to be a curved diamond. Comparisons of this yield curve with those from other methods show that it possesses almost all the advantages identified by the other methods. A new constitutive law is proposed, where the yield curve is a diamond and the flow rule is a combination of the normal and co-axial flow rule. The non-normal co-axial flow rule is necessary for the Coulombic yield constraint. This constitutive law not only captures the main features of forming LKFs but also takes the advantage of avoiding overestimating divergence during shear deformation. Moreover, this study provides a method for observing the flow rule for pack ice during deformation.

An elastic-viscoplastic constitutive model for the hot-forming of aluminum alloys

Under hot-forming conditions characterized by high homologous temperatures and strain-rates, metals usually exhibit rate-dependent inelastic behavior. An elastic-viscoplastic constitutive model is presented here to describe metal behavior during hot-forming. The model uses an isotropic internal variable to represent the resistance offered to plastic deformation by the microstructure. Evolution equations are developed for the inelastic strain and the deformation resistance based on experimental results. A methodology is presented for extracting model parameters from constant true strain-rate compression tests performed at different temperatures. Model parameters are determined for an Al-1Mn alloy and an Al-Mg-Si alloy, and the predictions of the model are shown to be in good agreement with the experimental data. (C) 2000 Kluwer Academic Publishers.

A Bilinear Constitutive Model for Isotropic Bimodulus Materials

Proper formulation of stress-strain relations, particularly in tension-compression situations for isotropic biomodulus materials, is an unresolved problem. Ambartsumyan's model [8] and Jones' weighted compliance matrix model [9] do not satisfy the principle of coordinate invariance. Shapiro's first stress invariant model [10] is too simple a model to describe the behavior of real materials. In fact, Rigbi [13] has raised a question about the compatibility of bimodularity with isotropy in a solid. Medri [2] has opined that linear principal strain-principal stress relations are fictitious, and warned that the bilinear approximation of uniaxial stress-strain behavior leads to ill-working bimodulus material model under combined loading. In the present work, a general bilinear constitutive model has been presented and described in biaxial principal stress plane with zonewise linear principal strain-principal stress relations. Elastic coefficients in the model are characterized based on the signs of (i) principal stresses, (ii) principal strains, and (iii) on the value of strain energy component ratio ER greater than or less than unity. The last criterion is used in tension-compression and compression-tension situations to account for different shear moduli in pure shear stress and pure shear strain states as well as unequal cross compliances.

Constitutive modeling of ice in the high strain rate regime

The objective of the present work is to propose a constitutive model for ice by considering the influence of important parameters such as strain rate dependence and pressure sensitivity on the response of the material. In this regard, the constitutive model proposed by Carney et al. (2006) is considered as a starting basis and subsequently modified to incorporate the effect of brittle cracking within a continuum damage mechanics framework. The damage is taken to occur in the form of distributed cracking within the material during impact which is consistent with experimental observations. At the point of failure, the material is assumed to be fluid-like with deviatoric stress almost dropping down to zero. The constitutive model is implemented in a general purpose finite element code using an explicit formulation. Several single element tests under uniaxial tension and compression, as well as biaxial loading are conducted in order to understand the performance of the model. Few large size simulations are also performed to understand the capability of the model to predict brittle damage evolution in un-notched and notched three point bend specimens. The proposed model predicts lower strength under tensile loading as compared to compressive loading which is in tune with experimental observations. Further the model also asserts the strain rate dependency of the strength behavior under both compressive as well as tensile loading, which also corroborates well with experimental results. (C) 2010 Elsevier Ltd. All rights reserved.

The effect of grain size on the high-strain, high-strain-rate behavior of copper

Copper with four widely differing grain sizes was subjected to high-strain-rate plastic deformation in a special experimental arrangement in which high shear strains of approximately 2 to 7 were generated. The adiabatic plastic deformation produced temperature rises in excess of 300 K, creating conditions favorable for dynamic recrystallization, with an attendant change in the mechanical response. Preshocking of the specimens to an amplitude of 50 GPa generated a high dislocation density; twinning was highly dependent on grain size, being profuse for the 117- and 315-mu m grain-size specimens and virtually absent for the 9.5-mu m grain-size specimens. This has a profound effect on the subsequent mechanical response of the specimens, with the smaller grain-size material undergoing considerably more hardening than the larger grain-size material. A rationale is proposed which leads to a prediction of the shock threshold stress for twinning as a function of grain size. The strain required for localization of plastic deformation was dependent on the combined grain size/shock-induced microstructure, with the large grain-size specimens localizing more readily. The experimental results obtained are rationalized in terms of dynamic recrystallization, and a constitutive equation is applied to the experimental results; it correctly predicts the earlier onset of localization for the large grain-size specimens. It is suggested that the grain-size dependence of shock response can significantly affect the performance of shaped charges.