Yield behavior of photoplastic materials

A mixture of flexible and rigid polyester resins has been used previously by Morris and Riley¹⁶ and by Zachary and Riley⁹ to model plastic deformations. The last of these papers furnished mechanical and optical properties under uniaxial tension and compression for several different mixture ratios of the polyester resins and also presents some results under multiaxial-stress conditions from thin cylinders under internal pressure. In a recent paper, Burger, Gomide and Scott¹⁴ used the rigid polyester resin at elevated temperature to model plastic deformations in upset rings; the behavior of the rigid polyester was verified with diametrically compressed disks and uniaxial-compression specimens. A very important similitude requirement for model to prototype scaling in photoplasticity work is that the macroscopic yield behavior of model and prototype materials must be the same. Thus, not only uniaxial tension and compression properties must be examined, but also yield properties under multiaxial-stress states have to be determined. The purpose of this paper is to provide additional information on the yield behavior of polyester mixtures which appear suitable for model studies of manufacturing methods such as rolling and extruding. For these processes, mixture ratio, test temperature and strain rate can be used to control the shape of the stress-strain curve and the yield behavior. The experimental procedure used to determine the initial yield locus of the photoplastic materials employed a new specimen geometry proposed by Arcan, Hashin and Voloshin¹⁸ which produces uniform biaxial-stress fields of opposite sign in one section of the specimen. Both polycarbonate and polyester materials were evaluated using this procedure and results are compared with those available in the technical literature.     

Loaded and unloaded optical response of polyester model materials

The optical behavior of mixtures of rigid and flexible polyester resins when loaded and unloaded under constant strain-rate and varying test temperature are characterized. New evidence about the photoplastic method of analyzing deformed but unloaded models is presented through experiments with tensile or compressive uniaxial specimens, diametrically compressed disks and beams under pure bending, which were analyzed during loading, unloading and after being unloaded.     

Anisotropic response of high-purity α-titanium: Experimental characterization and constitutive modeling

This paper presents a comprehensive experimental and theoretical investigation of the deformation behavior of high-purity, polycrystalline α-titanium under quasi-static conditions at room temperature. The initial material in this study was a cross-rolled plate with a strong basal texture. To quantify the plastic anisotropy and the tension–compression asymmetry of this material, monotonic tensile and compressive tests were conducted, on samples cut along different directions of the plate. A new anisotropic elastic/plastic model was developed to describe the quasi-static macroscopic response of the aggregate. Key in its formulation is the use of an anisotropic yield criterion that captures strength-differential effects and an anisotropic hardening rule that accounts for texture evolution associated to twinning. A very good agreement between FE simulations using the model developed and uniaxial data was obtained.     

Effects of microstructure on uniaxial strength asymmetry of open-cell foams

Based on the elongated Kelvin model, the effect of microstructure on the uniaxial strength asymmetry of open-cell foams is investigated. The results indicate that this asymmetry depends on the relative density, the solid material, the cell morphology, and the strut geometry of open-cell foams. Even though the solid material has the same tensile and compressive strength, the tensile and compressive strength of open-cell foams with asymmetrical sectional struts are still different. In addition, with the increasing degree of anisotropy, the uniaxial strength as well as the strength asymmetry increases in the rise direction but reduces in the transverse direction. Moreover, the plastic collapse ratio between two directions is verified to depend mainly on the cell morphology. The predicted results are compared with Gibson and Ashby''s theoretical results as well as the experimental data reported in the literature, which validates that the elongated Kelvin model is accurate in explaining the strength asymmetry presented in realistic open-cell foams.     

Axisymmetric micromechanics of elasticity-perfectly plastic fibrous composites under uniaxial tension loading

The uniaxial response of a continuous fiber elastic-perfectly plastic composite is modelled herein as a two-element composite cylinder. An axisymmetric analytical micromechanics solution is obtained for the rate-independent elastic-plastic response of the two-element composite cylinder subjected to tensile loading in the fiber direction for the case wherein the core fiber is assumed to be a transversely isotropic elastic-plastic material obeying Tsai-Hill's yield criterion, with yielding simulating fiber failure. The matrix is assumed to be an isotropic elastic-plastic material obeying Tresca's yield criterion. It is found that there are three different circumstances that depend on the fiber and matrix properties: (1) fiber yield, followed by matrix yielding; (2) complete matrix yield, followed by fiber yielding; and (3) partial matrix yield, followed by fiber yielding, followed by complete matrix yield. The order in which these phenomena occur is shown to have a pronounced effect on the predicted uniaxial effective composite response.     

Anisotropic damage–plasticity model for concrete

A material model for concrete is proposed here within the framework of a thermodynamically consistent elasto-plasticity–damage theory. Two anisotropic damage tensors and two damage criteria are adopted to describe the distinctive degradation of the mechanical properties of concrete under tensile and compressive loadings. The total stress tensor is decomposed into tensile and compressive components in order to accommodate the need for the above mentioned damage tensors. The plasticity yield criterion presented in this work accounts for the spectral decomposition of the stress tensor and allows multiple hardening rules to be used. This plastic yield criterion is used simultaneously with the damage criteria to simulate the physical behavior of concrete. Non-associative flow rule for the plastic strains is used to account for the dilatancy of concrete as a frictional material. The thermodynamic Helmholtz free energy concept is used to consistently derive dissipation potentials for damage and plasticity and to allow evolution laws for different hardening parameters. The evolution of the two damage tensors is accounted for through the use of fracture-energy-based continuum damage mechanics. An expression is derived for the damage–elasto-plastic tangent operator. The theoretical framework of the model is described here while the implementation of this model will be discussed in a subsequent paper.     

A Study on Hydraulic Autofrettage of Thick-Walled Cylinders Incorporating Bauschinger Effect

Pressure vessels which are subjected to cyclic external or internal high pressure are used in many fields of industry and need to be sure of reliability and safety. To ensure of reliability and safety, thick-walled cylinder, such as a cannon or nuclear reactor, is autofrettaged to induce advantageous residual stresses. The compressive residual stress which was introduced by autofrettage process acts to offset the tensile residual stress induced by internal pressure. It increases operating pressure and restrains crack initiation and crack propagation. As the autofrettage level increases, the magnitude of compressive residual stress at the bore also increases. However, the Bauschinger effect reduces the compressive residual stresses with prior tensile plastic strain, and decreases the beneficial autofrettage effect. There are some differences between theoretical solution considering elastic-perfectly material behavior and real autofrettage process results. The purpose of the present paper is to predict the accurate residual stress of SNCM 8 high strength steel using the Kendall model which was adopted by ASME Code. The tensile and uniaxial Bauschinger effect tests of SNCM 8 were performed to evaluate Bauschinger effect factor(BEF), thereafter this constant was used in calculating the residual stress. The residual stress distribution which is considering the Bauschinger effect was profiled using Kendall model, and the results were compared with the analytical and Finite Element analysis. The results were found that residual stress incorporating the Bauschinger effect at bore was smaller than ideal calculation. These results should be considered in designing pressure vessels.     

Mechanically alloyed nanocrystalline iron and copper mixture: behavior and constitutive modeling over a wide range of strain rates

A comprehensive study on the response of a nanocrystalline iron and copper mixture (80% Fe and 20% Cu) to quasi-static and dynamic loading is performed. The constitutive model developed earlier by Khan, Huang & Liang (KHL) is extended to include the responses of nanocrystalline metallic materials. The strain rate and grain size dependent behaviors of porous nanocrystalline iron-copper mixture were determined experimentally for both static and dynamic loading. A viscoplastic model is formulated by associating the modified KHL model (representing the fully dense matrix behavior), and Gurson's plastic potential which provides the yield criteria for porous material. Simulations of uniaxial compressive deformations of iron-copper mixture with different initial porosity, grain size and at a wide range of strain rate (10⁻⁴ to 10³ s⁻¹) are made. The numerical results correlate well with the experimental observations.     

A plasticity and anisotropic damage model for plain concrete

A plastic-damage constitutive model for plain concrete is developed in this work. Anisotropic damage with a plasticity yield criterion and a damage criterion are introduced to be able to adequately describe the plastic and damage behavior of concrete. Moreover, in order to account for different effects under tensile and compressive loadings, two damage criteria are used: one for compression and a second for tension such that the total stress is decomposed into tensile and compressive components. Stiffness recovery caused by crack opening/closing is also incorporated. The strain equivalence hypothesis is used in deriving the constitutive equations such that the strains in the effective (undamaged) and damaged configurations are set equal. This leads to a decoupled algorithm for the effective stress computation and the damage evolution. It is also shown that the proposed constitutive relations comply with the laws of thermodynamics. A detailed numerical algorithm is coded using the user subroutine UMAT and then implemented in the advanced finite element program ABAQUS. The numerical simulations are shown for uniaxial and biaxial tension and compression. The results show very good correlation with the experimental data.     

A photomechanics material for elastoplastic stress analysis

The object of this investigation was to develop a technique or method for elastoplastic stress analysis using the optical effects of transparent materials. Of paramount importance was the selection and characterization of a suitable model material. In particular, it was desirable that the material be able to undergo large plastic strains while, at the same time, exhibiting a suitable level of optical response. A mixture of flexible and rigid polyester resins was found suitable, i.e., the mixture exhibited large strains and good optical response. It was found that unload birefringence (fringe order immediately upon removal of load) could be used to determine strain for a uniaxial-stress field. In particular, it provided a means for evaluating stress- and strain-concentration factors. Comparisons with other methods showed that the proposed method was reliable and gave results that are similar to those by other means. The usefulness of the material and method for two- and three-dimensional problems awaits further study.     

Mechanical characterisation of a viscoplastic material sensitive to hydrostatic pressure

The present paper deals with the characterisation of the static mechanical behaviour of an energetic material all along its lifespan. The material behaviour is viscoplastic, damageable and sensitive to hydrostatic pressure. For such materials, existing models have generally been developed in the framework of transient dynamic behaviour. These models are not suitable for a static study. Therefore a specific experimental protocol and an associated model are developed. Characterisation is derived from both uniaxial compressive, tensile tests and triaxial tests. Plastic behaviour is described by means of a parabolic yield criterion and a new hardening law. Non-associated plastic flow rule and isotropic damage complete the model. The performance of the model is illustrated through the simulation of various loading paths.     

Critical Evaluation of a Constitutive Model for Glassy Polycarbonate

Polycarbonate (PC) is an important amorphous glassy polymer whose intrinsic uniaxial response exhibits all the features like strain softening and hardening at large deformations characteristic of this class of materials. Polycarbonate is significantly ductile and is capable of sustaining large plastic deformation. Constitutive models of PC, in order to be useful, should be able to faithfully model its elastic as well as plastic behaviour with as few undetermined parameters as possible. We assess the efficacy of a particular model of glassy polymers by fitting its parameters through usual uniaxial tensile and compressive tests and then using those parameters to model a fracture specimen in 3-dimensions. A range of experimental techniques like digital image correlation, photoelasticity and x-ray tomography are used to make careful quantitative comparisons with computer simulations. Our results indicate that in view of the small scale yielding situation prevalent in PC specimens even at high loads, a faithful prediction of the elastic parameters are sufficient for reproducing most global responses and deformation fields away from the crack. However, to predict fracture initiation, the deformation state within the small but significant fracture process zone needs to be reproduced. This cannot be done unless the entire uniaxial response is modelled to a reasonable degree of accuracy.     

The effect of the irregular interface geometry in deformation and fracture of a steel substrate–boride coating composite

Presented in this paper is a computational analysis of the mechanisms involved in plastic deformation and fracture of a composite with coating under compressive and tensile loading. Using a steel specimen surface-hardened by diffusion borating, a role of the irregular geometry of the interface between the base material and hardened surface layer is investigated. In order to describe the mechanical behavior of the steel substrate and brittle coating, use is made of a plastic flow model including isotropic strain hardening and a fracture model, respectively. Using the Huber fracture criterion, the model takes into account the difference in the critical strength values for different types of local compressive and tensile states. It is shown that the irregular, serrated shape of the substrate–coating interface retards propagation of a longitudinal crack into this coating and prevents it from spalling under external compression of this composite. It is found out that even in the case of a simple uniaxial compression of the mesovolumes of this composite the boride “teeth” are subjected to tensile stresses, whose values are comparable with those of the external compressive load, and the direction of crack propagation and the general fracture behavior largely depend on the external loading conditions.     

扭转塑性变形对6063铝合金拉伸力学性能的影响机理研究

扭转是一种常用的冷作硬化方法。本文通过实心圆轴扭转实验和预扭试件的单向拉伸实验,研究了扭转塑性变形程度对6063铝合金拉伸力学性能的影响。通过理论研究和硬度分析探究了造成这一影响的内在机理。结果表明,试件扭转后其内部形成的以屈服强度为特征参数的梯度结构,是造成预扭试件力学性能得到改善的根本原因。并且,扭转不同的角度,材料内部产生的梯度结构也是不同的。而不同的梯度结构对试件力学性能的影响则表现为后继拉伸屈服强度随预扭角度的增大而增大。为了预测预扭试件的后继拉伸力学行为,验证前述结论的正确性,建立了由内到外屈服强度逐渐变化的有限元模型。此模型代表了预扭转变形试件,对其施加位移载荷,模拟后继单向拉伸加载过程。模拟所得材料力学性能随扭转角的变化趋势与实验结果基本吻合,从而验证了扭转冷作硬化后,圆轴试件内部产生了以屈服强度为特征参数的梯度结构这一结论。同时,也提供了一种有效的预测材料扭转后拉伸力学性能的数值模拟方法。     

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.