Simple Uniaxial Tension Research Articles

Two-dimensional elasticity solution of elastic strips and beams made of functionally graded materials under tension and bending

This paper presents a theoretical approach to solve elastic problems of functionally graded materials (FGMs). For FGMs with exponential gradient, based on a two-dimensional theory of elasticity, a governing equation is derived by means of the Airy stress function method together with the strain compatibility equation. Simple uniaxial tension and bending are solved. For an FGM layer with transversely and/or vertically varying material properties, stress distribution and strain field under simple tension are determined according to two different assumptions. The obtained results indicate that for a thin elastic layer of thickness-wise gradient as a transition zone linking two dissimilar materials, there is a horizontal displacement difference across the transition zone due to mismatch of the material properties. In particular, when the thickness of the FGM layer reduces to zero, the horizontal displacement difference has a severe mismatch across the interface of two perfectly bonded dissimilar materials. An FGM beam subjected to a bending moment is also analyzed. The normal stress exhibits a nonlinear distribution and may arrive at its maximum tensile stress inside the beam, not at the surface. The obtained elasticity solution is useful for better understanding of the mechanical behaviors of FGMs subjected to different combined loads.

Microstructure evolution and mechanical behavior of a high strength dual-phase steel under monotonic loading

Transmission electron microscopy (TEM) microstructures of a high-strength dual-phase steel DP800 have been examined after moderate plastic deformations in simple shear and uniaxial tension. Special attention has been paid to the effect of the intergranular hard phase (martensite) on the microstructure evolution in the near-grain boundary regions. Quantitative parameters of dislocation patterning have been determined and compared with the similar characteristics of previously examined single-phase steels. The dislocation patterning in the interiors of the ferrite grains in DP800 steel is found to be similar to that already observed in the single-phase IF (Interstitial Free) steel whereas the martensite-affected zones present a delay in patterning and display very high gradients of continuous (gradual) disorientations associated with local internal stresses. The above stresses are shown to control the work-hardening of dual-phase materials at moderate strains for monotonic loading and are assumed to influence their microstructure evolution and mechanical behavior under strain-path changes.

Failure behaviour of grid-scored foam cored composite sandwich panels for wind turbine blades subjected to realistic multiaxial loading conditions

The load response and failure behaviour of ‘grid-scored’ sandwich panels used in wind turbine blades have been investigated. This paper presents the results of a combined experimental and numerical investigation of the load response and failure behaviour of a specific grid-scored foam cored composite sandwich panel configuration subjected to multiaxial quasi-static loading conditions that are representative for realistic loading conditions present in wind turbine blades. From the experimental evidence a criterion based on fracture mechanics has been proposed for predicting the onset of fracture in the resin grid. The criterion can be applied directly in conjunction with finite element modelling based on 3D solid elements where the resin grid in situ the core is fully modelled. However, since most full-scale blade models are based on first-order shear deformation theory where the core properties normally are homogenised a strain-based failure criterion is also proposed. The input for this failure criterion is the allowable resin grid strain, which can be obtained from a simple uniaxial tension test of a grid-scored sandwich beam specimen. The predictions of the criteria have been compared with the experimental observations, and a good correlation has been found.

Enhanced mechanical properties in a high-manganese austenitic steel through formation of nano grains, nanotwinned austenite grains, nano carbides and TRIP

In this work, a specific thermomechanical treatment was used to enhance mechanical properties of a high-manganese austenitic steel. Simple uniaxial tension tests revealed that the treated steel exhibits an outstanding strength (yield strength: 970MPa and tensile strength: 1384MPa) and ductility (fracture strain: 37%) synergy. Microstructural studies showed that several strengthening mechanisms contribute to mechanical properties of the treated steel, including nano grains, nano twinned austenite grains, nano carbides and TRIP. Stacking fault energy and strain-induced martensitic transformation were found to have an important role in appropriate adjustment of the strengthening mechanisms to achieve the optimum properties.

Experimental characterization of microstructure development during loading path changes in bcc sheet steels

Interstitial free sheet steels show transient work hardening behavior, i.e., the Bauschinger effect and cross hardening, after changes in the loading path. This behavior affects sheet forming processes and the properties of the final part. The transient work hardening behavior is attributed to changes in the dislocation structure. In this work, the morphology of the dislocation microstructure is investigated for uniaxial and plane strain tension, monotonic and forward to reverse shear, and plane strain tension to shear. Characteristic features such as the thickness of cell walls and the shape of cells are used to distinguish microstructural patterns corresponding to different loading paths. The influence of the crystallographic texture on the dislocation structure is analyzed. Digital image processing is used to create a “library” of schematic representations of the dislocation microstructure. The dislocation microstructures corresponding to uniaxial tension, plane strain tension, monotonic shear, forward to reverse shear, and plane strain tension to shear can be distinguished from each other based on the thickness of cell walls and the shape of cells. A statistical analysis of the wall thickness distribution shows that the wall thickness decreases with increasing deformation and that there are differences between simple shear and uniaxial tension. A change in loading path leads to changes in the dislocation structure. The knowledge of the specific features of the dislocation structure corresponding to a loading path may be used for two purposes: (i) the analysis of the homogeneity of deformation in a test sample and (ii) the analysis of a formed part.

Determination of the parameters of the Prony series in hyper-viscoelastic material models using the finite element method

This paper is devoted to the description of a newly developed methodology for the determination of the parameters of the Prony series in rubber compounds. Four hyperelastic constitutive equations were selected and combined with the Prony equation to describe the hyper-viscoelastic behaviour of a rubber compound. An in-house simple uniaxial tension test was designed and performed on the three rubber strips with the same length and different widths of 1, 2 and 3cm. The corresponding finite element meshes of these samples were developed using an adaptive meshing technique. The numerical result of the first sample was compared with experimental results of the associated experiment in conjunction with a Nelder–Mead Simplex optimization method to determine the parameters of the Prony equation. These parameters were further used for the simulation of the other two samples to show applicability and repeatability of the developed method. The comparison of the associated force–extension curves with the experimentally measured data of the two samples confirmed the accuracy and reliability of the predicted parameters by this technique.

Consistent formulation of the growth process at the kinematic and constitutive level for soft tissues composed of multiple constituents

Previous studies have investigated the possibilities of modelling the change in volume and change in density of biomaterials. This can be modelled at the constitutive or the kinematic level. This work introduces a consistent formulation at the kinematic and constitutive level for growth processes. Most biomaterials consist of many constituents and can be approximated as being incompressible. These two conditions (many constituents and incompressibility) suggest a straightforward implementation in the context of the finite element (FE) method which could now be validated more easily against histological measurements. Its key characteristic variable is the normalised partial mass change. Using the concept of homeostatic equilibrium, we suggest two complementary growth laws in which the evolution of the normalised partial mass change is governed by an ordinary differential equation in terms of either the Piola–Kirchhoff stress or the Green–Lagrange strain. We combine this approach with the classical incompatibility condition and illustrate its algorithmic implementation within a fully nonlinear FE approach. This approach is first illustrated for a simple uniaxial tension and extension test for pure volume change and pure density change and is validated against previous numerical results. Finally, a physiologically based example of a two-phase model is presented which is a combination of volume and density changes. It can be concluded that the effect of hyper-restoration may be due to the systemic effect of degradation and adaptation of given constituents.

Model modification and prediction of mechanical behaviour of fabrics in uniaxial tension

The objective of this study is to predict the mechanical behaviour of fabrics in uniaxial tensile using only their technical parameters. To achieve this objective, it was necessary, in first stage, to develop a model which can simulate this fabric mechanical behaviour. A modified form of a rheological model is used to describe the mechanical behaviour of fabrics in uniaxial tension. The proposed analytical model can fairly well replicate the behaviour of fabrics during relaxation and simple traction. In order to characterise the coefficients of this model, simple uniaxial tension and relaxation tests were performed for 29 fabrics in the warp and the weft directions. A retro‐propagation algorithm is applied in training the artificial neuronal network, which performs a functional mapping between these mechanical coefficients and the technical parameters of fabric. This allowed us to predict the mechanical behaviour in tension and relaxation of fabrics starting only from their technical parameters.

Influence of elastic T-stress on the growth direction of two parallel cracks

This paper studies fracture initiation direction of two parallel non-coplanar cracks of equal length. Using the dislocation pile-up modelling, singular integral equations for two parallel cracks subjected to mixed-mode loading are derived and the crack-tip field including singular and non-singular terms is obtained. The kinking angle is determined by using the maximum hoop stress criterion, or the <TEX>${\sigma}_{\theta}$</TEX>-criterion. Results are presented for simple uniaxial tension and biaxial loading. The biaxiality ratio has a noticeable influence on crack growth direction. For the case of biaxial tension, when neglecting the T-stress the crack branching angle is overestimated for small crack inclination angles relative to the largest applied principal stress direction, and underestimated for large crack inclination angles.

Softening hyperviscoelasticity for modeling rate-dependent material failure

New models of viscoelastic solids at small and finite deformations are proposed that describe material failure by enforcing the energy limiter — the average bond energy. Basically, the bond energy defines the energy that is necessary to separate two attracting particles. In the case of a solid composed of many particles there exists a magnitude of the average bond energy that is necessary to separate particles in a small material volume. The average bond energy can be calculated if a statistical distribution of the bond density is known for a particular material. Alternatively, the average bond energy can be determined in macroscopic experiments if the energy limiter is introduced in a material constitutive model. Traditional viscoelastic models of materials do not have energy limiters and, consequently, they allow for unlimited energy accumulation under the strain increase. The latter is unphysical, of course, because no material can sustain large enough deformations without failure. The average bond energy is the energy limiter that controls material softening, which indicates failure. Thus, by limiting the stored energy we include a description of material failure in the constitutive model. Viscoelasticity including energy limiters can be called softening hyperviscoelasticity. We present two softening hyperviscoelasticity models for small and finite deformations. In all cases the elastic and viscoelastic responses are described by potentials with limiters, which control material softening. The models are studied in the case of simple shear and uniaxial tension. The results of the calculations show that softening hyperviscoelasticity can be used for analysis of rate-dependent failure of materials.

Multiscale mechanics of TRIP-assisted multiphase steels: I. Characterization and mechanical testing

The mechanical behaviour of transformation-induced plasticity (TRIP)-assisted multiphase steels is addressed based on three different microstructures generated from the same steel grade. The mechanisms responsible for the work-hardening capacity and the resulting balance between strength and resistance to plastic localization are investigated at different length scales. The macroscopic mechanical response is determined by simple shear, uniaxial tension, Marciniak and equibiaxial tension supplemented by earlier tensile tests on notched and cracked specimens. It is shown that the transformation rate reaches a maximum for stress states intermediate between uniaxial tension and equibiaxial tension. At an intermediate length scale, the true in situ flow properties of the individual ferrite–bainite and retained austenite phases are determined by combining neutron diffraction and digital image correlation. This combined analysis elucidates the partitioning of stress and strain between the different constitutive phases. Based on these results, supplemented by transmission electron microscopy and electron backscattered diffraction observations, a general overview of the hardening behaviour of TRIP-assisted multiphase steels is depicted.

Observations of anisotropy evolution and identification of plastic spin parameters by uniaxial tensile tests

Micromechanical effects such as the development of crystallographic texture and of dislocation structures lead to evolution of material anisotropy during plastic deformation. The anisotropy of sheet metals is commonly quantified by its R-values. The R-value is defined as the ratio of the transverse strain to the thickness strain at a certain longitudinal strain, and it changes if the anisotropy changes. Conventional hardening models do not account for the evolution of anisotropy along an arbitrary orientation. Therefore, although R-values are measured from experiments, predictions of hardening behavior based on R-values using conventional hardening models do not reproduce the experiments for arbitrary orientation. The R-value evolution for large strains can be observed in simple uniaxial tension tests by measuring the transverse and longitudinal strains continuously up to large strains. A digital image correlation (DIC) method is introduced as superior to strain gages for measuring large strains. To model the experimental response, a rotational-isotropic-kinematic (RIK) hardening model is investigated. Because of this model’s ability to represent the rotational evolution of the anisotropy, it can predict the hardening behavior for non-RD and non-TD directions. Methods to identify the plastic spin and kinematic hardening parameters are also discussed.

Prediction of multiaxial mechanical behavior for conventional and highly crosslinked UHMWPE using a hybrid constitutive model

The development of theoretical failure, fatigue, and wear models for ultra-high molecular weight polyethylene (UHMWPE) used in joint replacements has been hindered by the lack of a validated constitutive model that can accurately predict large deformation mechanical behavior under clinically relevant, multiaxial loading conditions. Recently, a new Hybrid constitutive model for unirradiated UHMWPE was developed Bergström et al., (Biomaterials 23 (2002) 2329) based on a physics-motivated framework which incorporates the governing micro-mechanisms of polymers into an effective and accurate continuum representation. The goal of the present study was to compare the predictive capability of the new Hybrid model with the J 2-plasticity model for four conventional and highly crosslinked UHMWPE materials during multiaxial loading. After calibration under uniaxial loading, the predictive capabilities of the J 2-plasticity and Hybrid model were tested by comparing the load-displacement curves from experimental multiaxial (small punch) tests with simulated load-displacement curves calculated using a finite element model of the experimental apparatus. The quality of the model predictions was quantified using the coefficient of determination ( r 2). The results of the study demonstrate that the Hybrid model outperforms the J 2-plasticity model both for combined uniaxial tension and compression predictions and for simulating multiaxial large deformation mechanical behavior produced by the small punch test. The results further suggest that the parameters of the HM may be generalizable for a wide range of conventional, highly crosslinked, and thermally treated UHMWPE materials, based on the characterization of four material properties related to the elastic modulus, yield stress, rate of strain hardening, and locking stretch of the polymer chains. Most importantly, from a practical perspective, these four key material properties for the Hybrid constitutive model can be measured by relatively simple uniaxial tension or compression tests.

Neutron-diffraction measurement of the evolution of strain for non-uniform plastic deformation

Neutrons are particularly adept for the validation of modeling predictions of stress and strain. In recent years, there has been a significant effort to model the evolution of both the macroscopic stresses and the intergranular stress during plastic deformation. These have had broad implications with regard to understanding the evolution of residual stress and to diffraction-based measurements of strain. Generally the modeling and associated measurements have been performed for simple uniaxial tension, leaving questions with regard to plastic deformation under multi-axial stress and non-uniform stress. Extensive measurements of the strain profile across a plastic hinge for each of a series of loading and unloading cycles to progressively higher degrees of plastic deformation are presented. These measurements are used to assess multiple-length-scale finite-element modeling (FEM) of the plastic hinge, in which the elements will range in size from single crystallites (as used in successful simulations of uniaxial tension) to macroscopic elements (as typically used in FEM simulations).

Ductile tearing energy of aluminium alloy sheets determined by the single tensile testing (STT) method

Tearing energy of AA5050, AA3105 and AA8014 aluminium alloy sheets, having different mechanical characteristics, has been studied in simple uniaxial tension. The total energy required to tear the specimens was assumed to be composed of two components: one associated with uniform plastic deformation, which occurs in the work-hardening range of the material, and the other with post-uniform deformation and tearing which leads to the failure of the specimens. Tearing energy was calculated by subtracting the plastic deformation energy, dissipated in the uniform deformation range, from the total energy absorbed by the specimen during tension. The results have been analysed on the basis of the strain-hardening and strain-rate hardening parameters of the materials.

Failure Modes of Foams: The Influence of Orientation of Voids

An experimental investigation is undertaken in this paper for the assessment of the failure behavior of a series of polyurethane foams of variable specific density. All foamy materials examined here were acknowledged as transversely isotropic materials, whose axis of symmetry is, however, the weak axis of the medium. Simple uniaxial tension and compression tests were executed, and the experimental data were introduced into the elliptic paraboloid failure surface criterion. This condition was utilized for the comparison of the failure loci, associated with primary failure, of the polyurethane foams of different porosities. As a result, it is shown that, when the specific density of the foamy solids is raised, the shape, position and alignment of their failure loci intersections by the principal stress planes, as well as by the principal diagonal planes, is adjusted significantly. In addition to this fact, their degree of anisotropy is augmented; however, it is noted that the totality of the foamy materials tested exhibit solely compression-strong failure characteristics. Next, the influence of the voids’orientation on the failure modes of foams is investigated, by evaluating the variation of the essential parameters, required for the precise definition of the failure loci of the weak-axis polyurethanes, with respect to their specific density. And, further, by contrasting this variation with the respective one for the strong-axis foams encountered in previous studies of the senior author (Theocaris, 1992a,b; 1998). Hence, a comprehensive comparison of the failure behavior of foams, which display a weak and strong-axis of symmetry, is succeeded, revealing their similarities, but most importantly, their peculiarities and idiosyncrasies. Finally, a numerical analysis is disclosed as a means of determining the failure characteristics of mixed foams, that consist of both strong and weak-axis polyurethane materials of different specific densities. Accordingly, the effect of variation of the relative proportions and the specific densities of the constituent foamy phases on the characteristic parameters, designating the failure loci of mixed foams, is studied, offering interesting results concerning the modes of failure of such foams.

Effect of Hot Deformation under Complex Loading on the Transformation of Lamellar Type Microstructure in Ti-6.5Al-3.5Mo-1.6Zr-0.27Si Alloy

The transformation of the lamellar type microstructure to an equiaxed one in two-phase titanium alloys is determined not only by temperature-strain rate regimes but also by the modes of loading. The experimental results of investigations relating to the influence of one- and two-component monotonous loading on microstructure and mechanical behavior of the two-phase Ti-6.5Al-3.5Mo-1.6Zr-0.27Si titanium alloy are presented in this work. It is shown that under conditions of proportional torsion + tension loading the transformation of the lamellar microstructure occurs more uniformly in the transverse section of a sample and over its length than under conditions of simple torsion or uniaxial tension. The transformation is accompanied by formation of a typical texture based on the strain state. The following uniaxial tension in optimal temperature-strain rate regimes of superplasticity is characterized by a lower value of flow stress, uniform distribution of deformation and further microstructure transformation within the whole sample volume.

Multiaxial Cyclic Response of Filled Rubber

Abstract Cyclic response of filled rubber to simultaneous combinations of shear and extension is studied experimentally. Both in-phase (elastic) and out-of-phase (dissipative) portions of the response are measured for simple shear, uniaxial tension, and combinations of the two. As noted by other researchers, the response is nonlinear, with a strong dependence on strain amplitude. However, it is shown that the response to tension and to combinations of strains can be approximately related to the response to simple shear. Such correlations are useful in predicting the response of rubber-based components subjected to complex strain cycles when only experimental data on shear is available.

Effect of the molecular mass on the shear and longitudinal viscosity of linear polymers

The effect of the molecular mass of a polymer sample on the dependence of the stationary viscosity on the velocity gradient upon simple shear and uniaxial tension is studied. The model of the dynamics of a suspension of noninteracting dumbbells in the anisotropic medium is used. The theoretical results show that the asymptotic behavior of the shear viscosity does not depend on the molecular mass and corresponds to experimental data.

The structure and deformation behavior of zinc-rich coatings on steel sheet

The deformation behavior of commercially produced hot-dipped zinc and zinc-alloy coatings on steel under simple uniaxial tension has been studied. The strong basal plane texture of the hot-dipped galvanized coatings was found to be unfavorable for plastic flow and accounted for the extensive cracking observed during deformation. The eutectic structure in Galfan coatings was found to be beneficial in suppressing the formation of microcracks at low strain levels, although when grain boundary dents were present, cracks formed easily at these locations. Microcracks were observed in Galvalume coatings at all levels of strain. A technique to measure the coating plasticity has been developed to quantify the level of cracking in coatings at varying degrees of deformation.