Nonuniform Stress State Research Articles

Crack Initiation and Growth in PBX 9502 High Explosive Subject to Compression

Brittle and quasi-brittle solids, when subject to compression, fail by the development of microcracks that originate from heterogeneity. Lateral confinement has been shown to affect the failure pattern of the testing specimen, from splitting type of cracking with no confinement, to failure by shear banding with moderate confinement, to plasticitylike ductile failure when subject to high confining pressure. Even in the case of simple uni-axial compression, near local heterogeneity, e.g., pore or a small crack, the nonuniform stress state will introduce local confinement. As a result, different types of failure can occur simultaneously. In the present study, we investigate the process of damage initiation, accumulation, and cracking in a specimen of plastic bonded explosive (PBX), PBX 9502, containing a cavity and subject to compression. Due to the nonuniform deformation near the cavity, both tensile cracks and shear-dominated widespread material damage are generated. Detailed variation of quantities that characterize the process of crack initiation and growth will be presented and discussed.

Effect of treatment mode on fatigue resistance of material and thickness of the hardened surface

The vast majority of modern machine parts operate under cyclic loads, leading to, as a rule, failure, caused by the material fatigue. In this regard, the fatigue resistance of materials is one of the most important criteria for evaluating the structural strength of many parts of engineering structures. It is important that the process of exhaustion of cyclic life of metals, even at uniform stress state proceeds not uniformly in terms of volume of metal, but is initiated and develops more intensively in its surface layer. Under non-uniform stress state, role of the surface increases in connection with the presence of stress gradient. That's why, the most profound and systematic summarization of works, carried out in this direction, is aimed at performing a comprehensive analysis of changes in the properties of the surface layer of materials under active loading. However, investigated patterns of the surface microhardness change in the process of fatigue are usually qualitative and informative in nature. However, it should be noted that it is relevant to conduct studies, intended for obtaining quantitative estimates of the mentioned laws in order to develop fatigue failure criteria as a basis for improving calculation methods. This, in turn, requires developing a methodology for studying the surface layer behavior features and selecting the appropriate instrumental methods and tools. Analysis of a priori information indicates the need to investigate the microhardness, taking into account formation laws of the hardened surface layer, using different technological modes of surface treatment of metallic materials. In the present paper, the microhardness measuring method, characterized by a fairly high level of reproducibility of the obtained results and their experimentally justified correlation with the mechanical properties of the material is used. The developed method allows to determine the parameters of realized and residual life of the material.Thus, the research results, presented in the paper are of both scientific and practical interest. The authors have proposed the microhardness measuring methodology, characterized by a high level of reproducibility of the obtained results, which allows to determine the parameters of realized and the residual life of the material.

On the State of Stress in the Growth Plate under Physiologic Compressive Loading

The growth plate is a thin layer of cartilage sandwiched between epiphyseal and metaphyseal bone and is the location of active bone growth during childhood. It is subjected to large compressive and shear forces while protecting its resident chondrocytes from damage. We believe that computational modeling can help us better understand how the macro-scale loads are transmitted to micro-scale stresses and strains within the growth plate cartilage. As a first step in this process we analyzed the mechanical response of compression experiments performed on bovine bone/growth plate/bone samples. We endeavored to estimate the modulus of elasticity of the growth plate itself by simulating the compression experiments of these specimens using the finite element method. It is shown that when the growth plate in the compression specimens was modeled as a flat layer, the state of stress in the cartilage was triaxial and non-uniform with the hydrostatic stress being much greater than the octahedral shear stress over most of the central region of the growth plate test samples. The computational models accounted for variations in the average cartilage thickness, the non-uniaxial, non-uniform and triaxial state of stress in the thin cartilage layer, and for the estimated extrinsic compliance resulting from compression of the variable heights of bone on either side of the growth plate cartilage. However, due to lack of information on the internal structure of each sample, the models did not account for the variations in the non-flat topography of the growth plates. The models also did not include the calcified cartilage layer. Further model development is recommendedin order to determine the degree to which accounting for the complex growth plate topography influences the predicted cartilage modulus of elasticity.

Formation of Nanostructures in Brittle Materials with Transformations

Deformation and fracture of metal matrix composites under various loading schemes are studied. It is shown that in conditions far from transformation the material is deformed by dislocation glide as an ordinary crystal. In this case, yield stress is inversely proportional to the carbide spacing; in alloys with high solid phase content it is not achieved up lo fracture. Fracture of the material is catastrophically brittle. Deformation tests of composites near the phase transition temperature show that there are different transformations induced by a highly non-uniform stress state of the binding phase. Under loading the transformation scheme B2-> B2+ B19->B2 + "quasi-amorphous state" is realized in the binding phase with the formation of a microcrystalline, highly misoriented structure with the characteristic size of crystallites less than 10 nm. This structure has high plasticity and strong hardening. It governs an efficient transfer of external load to solid particles, inducing dislocation glide even in typically brittle titanium carbide particles. The physical meaning of using binders with unstable structure in composites involves a decrease in the scale of the structural level of plastic deformation due to the formation of the microcrystalline structure of the binding phase during non-uniform loading.

Modeling Induced Dislocation in Host Rocks around Excavations

The authors offer a new approach to modeling mining-induced dislocation in rock mass based on the calculation of nonuniform stress state of rocks, probabilistic assessment of rock mass strength and the laws of theory of percolation filtration.

Measurement of crack-tip and punch-tip transient deformations and stress intensity factors using Digital Gradient Sensing technique

The optical method of Digital Gradient Sensing (DGS) is extended to the study of fracture mechanics and impact mechanics problems. DGS is based on the elasto-optic effect exhibited by transparent materials subjected to non-uniform state of stress causing the angular deflection of light rays propagating through the material. Under plane stress conditions, the deflections of light rays can be related to two orthogonal in-plane stress gradients. In this paper, the principle of the method is presented first, followed by crack and punch experiments on PMMA plates for quantifying stress gradients near stress risers. The crack-tip stress intensity factors under both quasi-static and dynamic loading conditions are extracted from DGS measurements and are in good agreement with analytical and finite element results. The problem of a square-punch impacting the edge of a PMMA sheet is also studied using the new method by exploiting punch-tip–crack-tip analogy. The dynamic punch-tip stress intensity factors are extracted from the optical measurements and are again in good agreement with the ones from a complementary finite element analysis of the problem.

Comparison of Dynamic Moduli for Asphalt Mixtures Determined from Different Geometries and Compactions

Abstract The MEPDG (ARA, Inc., “NCHRP 1–37A Final Report: Guide for Mechanistic-Empirical Design of New and Rehabilitated Pavement Structures,” NCHRP Program 1–37A Project, National Research Council, Washington, D.C., 2004) introduces the dynamic modulus as the material property to characterize asphalt concrete. One of the challenges of acquiring the dynamic modulus from existing pavements is the standard dimensions of the test specimen. The specimen size specified in AASHTO TP62–07 (2007, “Standard Method of Test for Determining Dynamic Modulus of Hot-Mix Asphalt Concrete Mixtures,” AASHTO, Washington, D.C.) cannot be obtained from many pavement layers. This study evaluates two other geometries, indirect tension specimens and prismatic specimens, to determine whether the measured dynamic modulus is the same as the modulus obtained from TP62 protocol. This study provides a comparison of the effects of a non-uniform state of stress and anisotropy. These effects are isolated by comparing specimens prepared by Superpave gyratory compaction and vibratory steel-wheel compaction. The comparisons are verified using four 12.5-mm surface course mixtures with different aggregate shapes and binder types, and one 25.0-mm base mixture. The results show that the difference between the dynamic modulus values obtained from different geometries is statistically insignificant. The results provide justification for using alternative methods for acquiring the dynamic modulus experimentally—specifically, for previously constructed pavements.

Buckling of the composite orthotropic clamped–clamped cylindrical shell loaded by transverse inertia forces

The paper is concerned with the buckling analysis of the composite orthotropic cylindrical shell with clamped edges subjected to inertia loading. The problem is characterised by a non-uniform pre-buckling stress state. To address this, the relevant governing system of differential equations with variable coefficients has been derived and solved using Galerkin method. As a result, the problem of determining the critical acceleration causing the buckling of shell is reduced to the solution of the corresponding generalised eigenvalue problem. Using the proposed approach, the critical accelerations are calculated for the glass-fibre reinforced shells with various dimensional and stiffness parameters. Results of calculations are compared with those based on finite-element modelling and analysis.

Cyclic inelasticity and high-cycle fatigue of metals with consideration of the stress gradient effect*

Cyclic deformation behavior of metals and alloys under high-cycle loading in the nonuniform stress state is considered. A significant effect of the stress gradient on the cyclic inelastic deformation of the metal surface layers is shown. A model explaining the difference between the fatigue limits in the uniform and nonuniform stress states is proposed, which is based on accounting for the distinctions between cyclic stress–strain diagrams in the uniform and nonuniform stress states and for the fact that the fatigue limit is equal to the cyclic elasticity limit found for inelastic deformation typical of this class of materials.

Coupled experiment/finite element analysis on the mechanical response of porcine brain under high strain rates

This paper presents a coupled experimental/modeling study of the mechanical response of porcine brain under high strain rate loading conditions. Essentially, the stress wave propagation through the brain tissue is quantified. A Split-Hopkinson Pressure Bar (SPHB) apparatus, using a polycarbonate (viscoelastic) striker bar was employed for inducing compression waves for strain rates ranging from 50 to 750 s −1. The experimental responses along with high speed video showed that the brain tissue’s response was nonlinear and inelastic. Also, Finite Element Analysis (FEA) of the SHPB tests revealed that the tissue underwent a non-uniform stress state during testing when glue is used to secure the specimen with the test fixture. This result renders erroneous the assumption of uniaxial loading. In this study, the uniaxial volume averaged stress–strain behavior was extracted from the FEA to help calibrate inelastic constitutive equations.

인장시험을 유한요소해석 시뮬레이션하여 진응력-진변형도 곡선을 결정하는 방법

In the tensile test necking occurs at the maximum load point and non-uniform stress state is generated in this section. The equivalent stress becomes quite different from the axial stress as necking proceeds. Methods for obtaining the true stress-true strain curves, by overcoming difficulties due to the necking phenomena, have been developed by many authors. One of the methods based on the finite element analysis simulation is a very promising method. In this paper, general-purpose finite element program is used to simulate the tensile test. A round specimen and a flat specimen prepared from the same steel block are tested and simulated. The true stress-true strain curves are determined without assuming that the material follows Hollomon's law.

Fatigue and inelasticity of metals under nonuniform stressed state

Based on the review of the available publications and the findings of the original studies, the author demonstrates that with cyclic stresses in the maximum-stressed surface layer being equal the inelastic strains in the presence of stress gradients are smaller than those in the material under uniform stressed state. As a result, there is a difference in the cyclic stress–strain diagrams between these cases. An equation for the cyclic stress–strain diagram is put forward, which allows for the stress gradient effect. A model is substantiated, which provides an explanation for the difference between fatigue strength characteristics under uniform and nonuniform stressed states.

Fatigue of metals under nonuniform stressed state. part 2. methods of the analysis of research results

We review the currently available methods that are used to explain the difference in fatigue strength of metals and alloys under conditions of uniform and nonuniform stressed states. We discuss (i) the empirical methods, (ii) the methods allowing for the difference between nominal and effective cyclic stresses, (iii) the methods based on the notions of statistical theories of strength, and (iv) the methods assuming that responsible for fatigue failure are the averaged stresses in the surface layer. The calculated results are verified against experimental findings.

Fatigue of metals under nonuniform stressed state. Part 1. Stressed state assessment methods and results of investigation

We discuss the methods of assessment of stress-strain state and stress gradient in nonuniformly stressed structural components under elastic and elastic-plastic cyclic deformation. We systematize the research findings on fatigue of metals and alloys, including the stress concentration case, as well as the methods that describe the dependence of fatigue characteristics on the stress gradient.

Use of Nonuniform Stress-State Tests to Determine Fracture Energy of Asphalt Mixtures Accurately

Fracture energy of asphalt mixture is known to have a strong influence on the cracking performance of flexible pavement. Accurate determination of fracture energy of laboratory specimens requires accurate determination of strain through fracture, at the instant of fracture, on the plane where fracture occurs. Tests involving nonuniform stress states, such that the failure plane is known a priori, are suited for accurate and consistent determination of fracture energy because gauges from which strains can be determined can be placed directly on the failure plane. The Superpave&regd; indirect tension (IDT) test and the recently developed dog-bone direct tension (DBDT) test fall into this category. They were used in this study to determine tensile failure limits and, more specifically, to test whether fracture energy determined from one of the tests agreed with that from the other test and thereby indicated that fracture energy can be accurately determined from these tests. Strength tests were performed at constant rate of load ram displacement on dense- and open-graded asphalt mixtures for a range of temperature and aging conditions. Results showed that although tensile strength and failure strain between Superpave IDT and DBDT tests were different, because of differences in loading rate on the failure plane, the resulting fracture energy from the two tests was the same. This supports earlier findings that fracture energy is a fundamental property that is independent of stress state or loading conditions and, perhaps more important, that either one of these tests can be used to determine fracture energy of asphalt mixture accurately.

Anisotropic, non-uniform misfit strain in a thin film bonded on a plate substrate

Current methodologies used for the inference of thin film stresses through curvature measurements are strictly restricted to stress and curvature states which are assumed to remain uniform over the entire film/substrate system. These methodologies have recently been extended to non-uniform stress and curvature states for the thin film subject to non-uniform, isotropic misfit strains. In this paper we study the same thin film/substrate system but subject to non-uniform, anisotropic misfit strains. The film stresses and system curvatures are both obtained in terms of the non-uniform, anisotropic misfit strains. For arbitrarily non-uniform, anisotropic misfit strains, it is shown that a direct relation between film stresses and system curvatures cannot be established. However, such a relation exists for uniform or linear anisotropic misfit strains, or for the average film stresses and average system curvatures when the anisotropic misfit strains are arbitrarily non-uniform.

Anisotropic, non-uniform misfit strain in a thin film bonded on a plate substrate

Current methodologies used for the inference of thin film stresses through curvature measurements are strictly restricted to stress and curvature states which are assumed to remain uniform over the entire film/substrate system. These methodologies have recently been extended to non-uniform stress and curvature states for the thin film subject to non-uniform, isotropic misfit strains. In this paper we study the same thin film/substrate system but subject to non-uniform, anisotropic misfit strains. The film stresses and system curvatures are both obtained in terms of the non-uniform, anisotropic misfit strains. For arbitrarily non-uniform, anisotropic misfit strains, it is shown that a direct relation between film stresses and system curvatures cannot be established. However, such a relation exists for uniform or linear anisotropic misfit strains, or for the average film stresses and average system curvatures when the anisotropic misfit strains are arbitrarily non-uniform.

The Nonlinear Material Properties of Liver Tissue Determined From No-Slip Uniaxial Compression Experiments

The mechanical response of soft tissue is commonly characterized from unconfined uniaxial compression experiments on cylindrical samples. However, friction between the sample and the compression platens is inevitable and hard to quantify. One alternative is to adhere the sample to the platens, which leads to a known no-slip boundary condition, but the resulting nonuniform state of stress in the sample makes it difficult to determine its material parameters. This paper presents an approach to extract the nonlinear material properties of soft tissue (such as liver) directly from no-slip experiments using a set of computationally determined correction factors. We assume that liver tissue is an isotropic, incompressible hyperelastic material characterized by the exponential form of strain energy function. The proposed approach is applied to data from experiments on bovine liver tissue. Results show that the apparent material properties, i.e., those determined from no-slip experiments ignoring the no-slip conditions, can differ from the true material properties by as much as 50% for the exponential material model. The proposed correction approach allows one to determine the true material parameters directly from no-slip experiments and can be easily extended to other forms of hyperelastic material models.

Description of brittle failure of non-uniform MEMS geometries

The description of probability of failure of polysilicon micromachined components with complex geometries using a single set of Weibull parameters was investigated. Strength data from both uniform tension and from twelve non-uniform specimen geometries with central perforations were employed. These perforations allowed for twelve different combinations of stress concentration factors and radii of curvature. Two methods were applied to determine the Weibull parameters: in the first method, only the strength data from uniform tension specimens were used to determine the Weibull modulus and the material scale parameter. In the second approach, the strength data from all non-uniform tension geometries were used to calculate the material scale parameter and the Weibull modulus using the maximum likelihood method. The non-uniform stress state in each perforated specimen was taken into account through an elasticity finite element model and the use of the integral form of the Weibull probability function. Using the first method, an analysis considering active flaw populations at the top specimen surface or the specimen sidewalls indicated that the active flaw population is not the same at all scales: for 1–3 μm radius perforations and small stress concentration factor ( K = 3) the active flaw population was located at the specimen top surface, e.g. surface roughness, which, as the analysis indicated, was also the case for uniform tension specimens. For higher stress concentration factors (nominal K = 6 and 8) the analysis indicated that the active flaw population was located at the hole sidewall surface. As a result, for a given material the geometry of the specimen and the local state of stress determine the active flaw population from all flaws generated during fabrication and processing. Therefore, it is important that all potential failure modes be considered when extrapolations to other geometries and loadings are made using the Weibull probability function.

Concrete Subjected to Triaxial Stress States: Application to Pull-Out Analyses

This paper presents the application of three-dimensional (3D) -constitutive models for concrete formulated in the framework of plasticity theory to structural analyses of anchor devices. For this purpose, two commonly employed concrete material models are considered. The first model, the extended Leon model, is based on one yield surface for the description of compressive and tensile failure of concrete. The second material model is a multisurface plasticity model consisting of three Rankine yield surfaces and a Drucker-Prager yield surface. The predictive capability of the models is demonstrated by means of anchor devices, commonly employed in structural engineering for the connection of steel and concrete members. Such devices induce strongly nonuniform triaxial stress states in the surrounding concrete, ranging from tensile, overcompressive, to confined compressive stress states. In the vicinity of the anchor head, even nearly hydrostatic stress states may occur. The numerical simulations on the basis of the employed 3D material models for concrete give insight into the load-carrying behavior of the investigated anchor devices. Two headed studs characterized by different shapes of the anchor head and an undercut anchor are considered. Comparison of the peak loads and failure modes of the respective anchor device predicted by the numerical models with experimental data highlight the strength and weakness of the employed material models. It is shown that some load cases may lead to rather large differences in peak load depending on the choice of material model. These differences are based on the individual properties of the constitutive models for concrete and, hence, detailed knowledge of the model under consideration is essential for giving accurate estimates of the peak load of the anchor device and the failure mode of concrete.