Measurement and analysis of differential work hardening behavior of pure titanium sheet using spline function

Biaxial stress tests and in-plane tension/compression tests of pure titanium sheet (JIS #1) have been carried out in order to elucidate its anisotropic plastic deformation behavior under linear stress paths. Contours of plastic work and the directions of plastic strain rates at different levels of plastic work have been precisely measured in the stress space. The measured work contours bulged significantly toward the equibiaxial direction and showed strong asymmetry, and moreover, changed its shapes significantly with increasing plastic work (differential work hardening). Using the data of the measured work contours, the applicability of selected anisotropic yield functions, i.e., Hill’s quadratic, the Yld2000-2d and Cazacu’s yield functions, to the accurate prediction of the plastic deformation behavior of the pure titanium has been discussed. It was found that these yield functions were not able to reproduce the measured data. A new method for analyzing the differential work hardening behavior of the pure titanium sheet has been developed. This method uses the spline function of Bezier curves which approximates a work contour, inspired by the methodology proposed by Vegter and Boogaard (Int. J. Plasticity 22 (2006) 557-580). The procedure for determining the spline function is described in detail. The calculated results have been in good agreement with the differential work hardening behavior of the pure titanium sheet.     

On elastic–plastic fracture behavior of a bi-layered composite plate with a sub-interface crack under mixed mode loading

A generalized Irwin model is proposed to investigate elastic–plastic fracture behavior of a bi-layered composite plate with a sub-interface crack under combined tension and shear loading. The dependence of the stress intensity factors, the plastic zone size, the effective stress intensity factor and the crack tip opening displacement on the crack depth h, the Dundurs’ parameters and the phase angle θ is discussed in detail. Numerical results show that in most cases, if the crack is embedded in a stiffer material, when the crack is close to the interface, the plastic zone size and the crack tip opening displacement will increase. On the contrary, if the crack is embedded in a softer material, when the crack is close to the interface, the plastic zone size and the crack tip opening displacement will decrease.     

Constitutive modelling of fibre-reinforced composites with unidirectional plies using a plasticity-based approach

This paper presents the development of a constitutive model able to accurately represent the full non-linear mechanical response of polymer-matrix fibre-reinforced composites with unidirectional (UD) plies under quasi-static loading. This is achieved by utilising an elasto-plastic modelling framework. The model captures key features that are often neglected in constitutive modelling of UD composites, such as the effect of hydrostatic pressure on both the elastic and non-elastic material response, the effect of multiaxial loading and dependence of the yield stress on the applied pressure.The constitutive model includes a novel yield function which accurately represents the yielding of the matrix within a unidirectional fibre-reinforced composite by removing the dependence on the stress in the fibre direction. A non-associative flow rule is used to capture the pressure sensitivity of the material. The experimentally observed translation of subsequent yield surfaces is modelled using a non-linear kinematic hardening rule. Furthermore, evolution laws are proposed for the non-linear hardening that relate to the applied hydrostatic pressure.Multiaxial test data is used to show that the model is able to predict the non-linear response under complex loading combinations, given only the experimental response from two uniaxial tests.     

Modeling hysteresis behavior of cross-ply C/SiC ceramic matrix composites

In this paper, the loading/unloading tensile behavior of cross-ply C/SiC ceramic matrix composites at room temperature has been investigated. The loading/unloading stress–strain curve exhibits obvious hysteresis behavior. An approach to model the hysteresis loops of cross-ply ceranic matrix composites including the effect of matrix cracking has been developed. Based on the damage mechanisms of fiber sliding relative to matrix during unloading and subsequent reloading, the unloading interface reverse slip length and reloading interface new slip length of different matrix cracking modes are obtained by the fracture mechanics approach. The hysteresis loops of cross-ply C/SiC ceramic matrix composites corresponding to different peak stresses have been predicted.     

Microscopic failure mechanisms of fiber-reinforced polymer composites under transverse tension and compression

The mechanical behavior of unidirectional fiber-reinforced polymer composites subjected to tension and compression perpendicular to the fibers is studied using computational micromechanics. The representative volume element of the composite microstructure with random fiber distribution is generated, and the two dominant damage mechanisms experimentally observed – matrix plastic deformation and interfacial debonding – are included in the simulation by the extended Drucker–Prager model and cohesive zone model respectively. Progressive failure procedure for both the matrix and interface is incorporated in the simulation, and ductile criterion is used to predict the damage initiation of the matrix taking into account its sensitivity to triaxial stress state. The simulation results clearly reveal the damage process of the composites and the interactions of different damage mechanisms. It can be concluded that the tension fracture initiates as interfacial debonding and evolves as a result of interactions between interfacial debonding and matrix plastic deformation, while the compression failure is dominated by matrix plastic damage. And then the effects of interfacial properties on the damage behavior of the composites are assessed. It is found that the interfacial stiffness and fracture energy have relatively smaller influence on the mechanical behavior of composites, while the influence of interfacial strength is significant.     

Analytical evaluation on uniaxial tensile deformation behavior of fiber metal laminate based on SRPP and its experimental confirmation

Uniaxial tensile tests have been carried out to accurately evaluate the in-plain mechanical properties of fiber metal laminates (FMLs). The FMLs in this paper comprised of a layer of self-reinforced polypropylene (SRPP) sandwiched between two layers of aluminum alloy 5052-H34. In this study, nonlinear tensile and fracture behavior of FMLs under in-plane loading conditions has been investigated with numerical simulations and theoretical analysis. The numerical simulation based on finite element modeling using the ABAQUS/Explicit and the theoretical constitutive model based on the volume fraction approach using the rule of mixture and the modified classical lamination theory, which incorporates the elastic–plastic behavior of the aluminum alloy and SRPP, are used to predict the in-plain mechanical properties such as stress–strain response and deformation behavior of the FMLs. In addition, the pre-stretching process is used to reduce the thermal residual stresses before the uniaxial tensile tests of the FMLs. Through comparing the numerical simulations and the theoretical analysis with the experimental results, it is concluded that the adopted numerical simulation model and the theoretical approach can describe with sufficient accuracy of the actual tensile stress–strain curve.     

Non-orthogonal stress modes for interfacial fracture based on local plastic dissipation

Interfacial cracks have several features which are different from those of cracks in homogeneous materials. Among those, the loading mode dependency of interfacial toughness has been a main obstacle to the widespread utilization of interfacial fracture mechanics. In this study, plasticity-induced toughening of an interface crack between an elastic–plastic material and an elastic material is studied. A useful relationship between the plastic dissipation and the plastic zone size is derived via an effective crack length model. Non-orthogonal stress modes for interface cracks are proposed on the basis of the plastic dissipation mechanism and a mixed-mode criterion for interfacial crack growth is also proposed using these stress modes. The non-orthogonal stress modes are able to represent the asymmetric behavior, mode-dependent toughening and ε-dependency of interfacial crack growth.     

Micro-mechanical modeling the densification behavior of titanium metal matrix composites

Vacuum hot pressing has been used for the development of Ti-MMCs using foil–fiber–foil method, and a unified micro-mechanical model has been presented to determine the densification behavior. The effects of processing conditions on the consolidation, together with microstructural evolutions of the materials have been investigated. The explicit representation of fiber array, which is coupled with deformation behavior of matrix materials, is modeled in finite element simulation to determine the effect of geometrical arrangements on densification process. The approach is then used to model the densification behavior of porous plastic materials using the parameters obtained, and comparisons are made with experimental data. As shown by the results, either increasing temperature or pressure leads to increasing densification rate but the conditions should be determined by the precisely controlled geometrical arrangements with processing conditions. Further experimental investigation of the densification behavior of SiC/Ti–6Al–4V composites using thermo-acoustic emission analysis has been performed, and the results obtained are compared with the model predictions. Good comparisons are achieved.     

Non-orthogonal stress modes for interfacial fracture based on local plastic dissipation

Interfacial cracks have several features which are different from those of cracks in homogeneous materials. Among those, the loading mode dependency of interfacial toughness has been a main obstacle to the widespread utilization of interfacial fracture mechanics. In this study, plasticity-induced toughening of an interface crack between an elastic-plastic material and an elastic material is studied. A useful relationship between the plastic dissipation and the plastic zone size is derived via an effective crack length model. Non-orthogonal stress modes for interface cracks are proposed on the basis of the plastic dissipation mechanism and a mixed-mode criterion for interfacial crack growth is also proposed using these stress modes. The non-orthogonal stress modes are able to represent the asymmetric behavior, mode-dependent toughening and ε-dependency of interfacial crack growth.     

A constitutive model for the uplift behavior of anchors in cohesionless soils

Abstract

A series of triaxial tests has been performed to establish the stress‐strain curves for I‐Lan sand and Taipei silty sand. A constitutive model for the continuous strain hardening‐softening and volumetric dilatancy of these two soils is proposed, based on the results of triaxial tests. Using this model, a numerical program is then established, with FLAC software, to analyze the uplift behavior of model anchors in sand and field anchors in silty soil.

It was found from triaxial tests, that the peak friction angle increases with relative density of soil and decreases with confining pressure. A non‐associated flow rule between plastic strain increment and stress tensor was found. As accumulative plastic strain, relative density and confining pressure were changed, the mobilized friction angle and mobilized dilatancy angle also changed. All parameters needed for the proposed model can be expressed as functions of relative density and confining pressure. This model can calculate the stress‐ strain curves of cohesionless soils determined from triaxial tests accurately.

The load‐displacement behaviors determined from anchor tests are compared with those calculated from this numerical program, the numerical results are in good agreement with the test results not only for model anchors in sand but also for different types of field anchors in silty soil.     

Development of viscoelastic/rate-sensitive-plastic constitutive law for fiber-reinforced composites and its applications. Part I: Theory and material characterization

The viscoelastic/rate-sensitive plastic constitutive law to describe the nonlinear, anisotropic/asymmetric and time/rate-dependent mechanical behavior of fiber-reinforced (sheet) composites was developed under the plane stress condition. In addition to the theoretical aspect of the developed constitutive law, experiments to obtain the material parameters were also carried out for the woven fabric composite based on uni-axial tension and compression tests as well as stress relaxation tests, while the numerical formulation and verifications with experiments are discussed in Part II.     

Characterizing and modeling the non-linear viscoelastic tensile deformation of a glass fiber reinforced polypropylene

On the basis of comprehensive experimental investigations on a long glass fiber reinforced polypropylene (PP-LGF) a novel rheological material model is developed. It features a decomposition of the stress into a time independent quasi-static and a time and strain dependent viscous contribution. Furthermore it allows for plastic deformations starting from the very beginning of straining and is thereby able to reproduce the absence of a purely linear elastic domain going along with the nonexistence of a defined yield point, characteristic for many fiber reinforced thermoplastic polymers. In order to approach the true quasi-static material behavior, various tensile tests were carried out. The viscous material behavior was deduced from a series of stress relaxation experiments and is described by Eyring’s equation with strain dependent viscosity parameters.     

Geometry and grain size effects on the fracture behavior of sheet metal in micro-scale plastic deformation

The demand on micro-parts is significantly increasing in the last decade due to the trend of product miniaturization. When the part size is scaled down to micro-scale, the billet material consists of only a few grains and the material properties and deformation behaviors are quite different from the conventional ones in macro-scale. The size effect phenomena occur in micro-scale plastic deformation or micro-forming and there are still many unknown phenomena related to size effect, including geometry and grain size effects. It is thus critical to investigate the size effect on deformation behavior, especially for the fracture behavior in micro-scale plastic deformation. In this research, tensile test was conducted with annealed pure copper foils with different thicknesses and grain sizes to study the size effects on fracture behavior. It is found that flow stress, fracture stress and strain, and the number of micro-voids on the fracture surface decrease with the decreasing ratio of specimen size to grain size. Based on the experimental results, dislocation density based models which consider the interactive effect of specimen and grain sizes on fracture stress and strain are developed and their accuracies are further verified and validated with the experimental results obtained from this research and prior arts.     

Anisotropic damage behavior of SiC/SiC composite tubes: Multiaxial testing and damage characterization

The results of a large experimental campaign concerning the mechanical behavior of SiC/SiC composites tubes under uniaxial and biaxial loadings (both tension–torsion and tension-internal pressure) are presented. The anisotropy of the elastic moduli, damage onset and failure properties has been characterized. The orientation of matrix cracking was analyzed, based on surface observations, and its connection to the macroscopic stress–strain response provides important insight into the underlying deformation mechanisms. However, the macroscopic behavior still exhibits unexplained features, and mechanisms specific to the textile architecture are proposed.     

Development of new cyclic plasticity model for 304LN stainless steel through simulation and experimental investigation

Cyclic plastic deformation characteristics of 304LN stainless steel material have been studied with two proposed cyclic plasticity models. Model MM-I has been proposed to improve the simulation of ratcheting phenomenon and model MM-II has the capability to simulate both cyclic hardening and softening characteristics of the material at various strain ranges. In the present paper, strain controlled simulations are performed with constant, increasing and decreasing strain amplitudes to verify the influences of loading schemes on cyclic plasticity behaviors through simulations and experiments. It is observed that the material 304LN exhibits non Masing characteristics under cyclic plastic deformation. The measured deviation from Masing is well established from the simulation as well as from experiment. Simulation result shows that the assumption of only isotropic hardening is unable to explain the hardening or softening characteristics of the material in low cycle fatigue test. The introduction of memory stress based cyclic hardening coefficient and an exponentially varying ratcheting parameter in the recall term of kinematic hardening rule, have resulted in exceptional improvement in the ratcheting simulation with the proposed model, MM-II. Plastic energy, shape and size of the hysteresis loops are additionally used to verify the nature of cyclic plasticity deformations. Ratcheting test and simulation have been performed to estimate the accumulated plastic strain with different mean and amplitude stresses. In the proposed model MM-I, a new proposition is incorporated for yield stress variation based on the memory stress of loading history along with the evolution of ratcheting parameter with an exponential function of plastic strain. These formulations lead to better realization of ratcheting rate in the transient cycles for all loading schemes. Effect of mean stress on the plastic energy is examined by the simulation model, MM-I. Finally, the micro structural investigation from transmission electronic microscopy is used to correlate the macroscopic and microscopic non Masing behavior of the material.     

Prestressed natural fibre spun yarn reinforced polymer-matrix composites

We report that a prestressing technique similar to that traditionally used in prestressed concrete can improve the mechanical performance of flax fibre spun yarn reinforced polymer-matrix composites. Prestressing a low twist yarn not only introduces tension to the constituent fibres and compressive stress to the matrix similar as in prestressed concretes, but also causes changes to the yarn structure that lead to the rearrangement of fibres within the yarn. Prestressing increases the fibre packing density in yarn, causes fibre straightening, and reduces fibre obliquity in yarn (improved fibre alignment along yarn axis). All these changes contribute positively to the mechanical properties of the natural fibre yarn reinforced composites.     

Effect of elastic–plastic matrix on thermo-mechanical response of continuous anisotropic fiber-reinforced composites

Based on a concentric cylinder model, the analytical elastic–plastic solution of deformations and stresses for the composites reinforced with transversely isotropic, circumferentially orthotropic and radially orthotropic fibers subjected to axisymmetric thermo-mechanical loading is developed. How the plasticity, volume fraction, physical and mechanical properties of the matrix affect the elastic–plastic thermo-mechanical response of the composites is investigated. The plasticity of the matrix decreases greatly the axial compressive stress in the matrix, but more noticeably increases the axial compressive stress in the fiber. For the composites reinforced with transversely isotropic, circumferentially orthotropic and radially orthotropic fibers, decreasing the volume fraction, thermal expansion coefficient and Young's modulus, and increasing the yield stress and hardening parameter of the matrix can lower the maximum equivalent stress of the fiber. However, increasing the yield stress and hardening parameter of the matrix raises the maximum equivalent stress of the matrix.     

Local stress field approach for post cracking analysis of FRP strengthened RC elements

A computational framework previously presented for nonlinear analysis of RC elements, has been developed for FRP strengthened RC elements in this study. With the aim of the developed model nonlinear behavior of strengthened RC elements can be simulated based on local stresses state at the crack surface considering all stress transfer mechanisms. Moreover, the local response of each component and its effect on the global behavior of the element can be obtained which is useful for proposing rational design relations. The versatility of the proposed method is verified by comparing the analytical and experimental results. Based on the analytical results, a simple relation is proposed for shear design and assessment of FRP strengthened RC elements and members. The accuracy of the proposed design relation is verified against available experimental results on FRP strengthened RC beams.     

Dynamic micromechanical modeling of textile composite strength under impact and multi-axial loading

Micromechanical finite element modeling has been employed to define the failure behavior of S2 glass/BMI textile composite materials under impact loading. Dynamic explicit analysis of a representative volume element (RVE) has been performed to explore dynamic behavior and failure modes including strain rate effects, damage localization, and impedance mismatch effects. For accurate reflection of strain rate effects, differences between an applied nominal strain rate across a representative volume element (RVE) and the true realized local strain rates in regions of failure are investigated. To this end, contour plots of strain rate, as well as classical stress contours, are developed during progressive failure. Using a previously developed cohesive element failure model, interfacial failure between tow and matrix phases is considered, as well as classical failure modes such as fiber breakage and matrix microcracking. In-plane compressive and tensile loading have been investigated, including multi-axial loading cases. Highly refined meshes have been employed to ensure convergence and accuracy in such load cases which exhibit large stress gradients across the textile RVE. The effect of strain rate and phase interfacial strength have been included to develop macro-level material failure envelopes for a 2D plain weave and 3D orthogonal microgeometry.     

On the Lewis–Nielsen model for thermal/electrical conductivity of composites

Several models have been proposed in the literature to describe the thermal and electrical conductivities of particulate composites. Among the proposed models, the Lewis–Nielsen model appears quite attractive as it is simple to use and it predicts the correct behavior when filler concentration () approaches the maximum packing concentration (_m). In this paper, the Lewis–Nielsen model is evaluated in light of a vast amount of experimental data available on thermal and electrical conductivities of particulate composites. The Lewis–Nielsen model is found to describe the experimental data for both thermal and electrical conductivities reasonably well.