Mechanical Response and Energy Absorption of 316L Stainless Steel Body-Centered-Cubic Functionally Graded Lattice Structures under Quasistatic Compressive Test

Five different density gradient variation strategies are proposed for body-centered-cubic (BCC) lattice structures in parallel to the loading direction prepared by selective laser melting with 316 L stainless steel as the building material, and the mechanical properties, deformation behavior, and energy absorption capacity of lattice structures with different density gradient variations and uniform lattice structure under compressive loading are investigated and compared. The results show that the elastic modulus and compressive strength of the uniform lattice structure are better than those of the lattice structure with density gradient parallel to the loading direction, provided that the relative densities are similar. However, through a reasonable design of density gradient, the lattice structure with density gradient parallel to the loading direction can obtain higher plateau stress than the uniform lattice structure and increase the onset densification strain to a certain extent, which obviously improves the energy absorption capacity of the lattice structure. The results obtained by finite-element calculations are in good agreement with the experimental results and can better restore the deformation behavior of the lattice structure under compressive loading. This work provides inspiration for the design of the density gradient of the lattice structure.     

Residual stress gradients along ion implanted zones — cubic crystals

Large internal strains and stresses can be produced by low temperature implantation over small distances from the free surface in a thick substrate. These are typically non-uniform and have large composition gradients. In dilute bcc solutions, containing unclustered interstitial implants, the residual macroscopic strains may be treated as isotropic. The calculation of residual strain (or stress) is based upon anisotropic elasticity theory and internal stress is given in terms of the dipole tensor for individual defects in single crystal films. In a completely elastic zone, forces act to maintain a rigid outside surface and cause the strain distribution to be zero along directions parallel to the free surface. This produces a strain magnification along the perpendicular direction from Poisson contractions. If the implanted zone is completely relaxed by plastic deformation, the strains are described by the free expansion strains due to both implants and lattice damage. There is no angular dependence of the free expansion strain in this extreme condition. One can determine whether a zone is completely elastic, completely relaxed by plastic deformation, or in some intermediate state from plots of strain against sin², where is the angle of tilt relative to the surface normal. These results may be obtained from X-ray Bragg intensity data by measuring shifts and line broadening from (hkl) planes at different tilt angles. Theoretical results are given for both single crystal and polycrystalline materials in terms of residual strain and stress.     

A circular inhomogeneity with interface slip and diffusion under in-plane deformation

We consider the in-plane deformation of a circular elastic inhomogeneity embedded in an infinite elastic matrix subjected to remote uniform stresses or uniform heat flow. The inhomogeneity and matrix have different material properties. The rate-dependent slip and mass transport by stress-driven diffusion concurrently occur on the inhomogeneity/matrix interface. For the remote uniform stress case, it is observed that the internal stresses within the inhomogeneity are quadratic functions of the coordinates x and y, and decay with two relaxation times. Interestingly the average mean stress within the circular inhomogeneity is in fact time-independent. As time approaches infinity, the internal stress field within the inhomogeneity becomes uniform and hydrostatic. In addition the change of strain energy due to the introduction of the circular elastic inhomogeneity is derived, containing various existing results as special cases. Furthermore, a simple condition leading to an internal uniform stress state within the inhomogeneity is found. This condition, which is independent of the elastic properties of the inhomogeneity and matrix, gives a simple relationship between the interface drag and diffusion parameters. For the remote heat flow case, the internal thermal stresses are linear functions of the coordinates x and y and decay only with a single relaxation time. Numerical results are presented to demonstrate the obtained solution and the corresponding physics.     

Understanding local deformation in metallic polycrystals using high energy X-rays and finite elements

A methodology for understanding the stress and elastoplastic deformation responses within a loaded polycrystal is presented along with illustrative examples. High energy synchrotron X-rays are used to penetrate bulk metallic samples and produce diffracted intensity from each deforming crystal – revealing the evolving internal structure. A virtual representation of the microstructure is constructed using the finite element method (FEM) to simulate the evolution of the elastoplastic deformations, stress fields, and lattice orientations within the deforming crystals as the polycrystal is loaded. Simulations are compared directly to experimental diffraction data. In the case of powder experiments, lattice strain pole figures (SPFs) measured experimentally are compared to SPFs calculated by projecting X-rays through the finite element mesh. During in situ loading experiments, the stress states are found to differ from one crystal to the next and to vary from the stress being applied at the macroscale. A SPF/FEM-based methodology for quantifying residual stress fields within processed polycrystalline components is described. SPFs were measured at many points within a shrink-fit sample. Finite element discretizations of both the sample and orientation space of each diffraction volume were used to formulate an optimization for the distribution of the stress tensor within the sample. A different experiment, one in which the X-ray beam and the crystals are closer to the same size, is used to investigate the aggregate crystal by crystal. The Debye–Scherrer rings reduce to a set of spots associated with each crystal within the diffraction volume. This method is demonstrated by tracking deformation of four grains within a deforming BCC titanium aggregate loaded in situ within the elastic regime to determine the single crystal elastic moduli. Plastic deformation can also be investigated by monitoring the size and shape of individual diffraction spots. Each spot contains geometrically exact information regarding the internal structure of the crystal. Instead of reconstructing the crystal structure by inverting the diffraction data, virtual diffraction experiments are performed on the finite element mesh and the resulting simulated diffraction patterns are compared directly to the experimental results. Once the experimental/simulation methodology is validated, the approximation of the subgrain distribution of stress and lattice orientation from the finite element model can be used to construct theories for failure phenomena such as microcrack initiation. As opposed to other methods of discretizing a polycrystalline aggregate, the finite element framework enables a seamless transition to analyses associated with mechanical design.     

Evolution and analysis of γ′ rafting during creep of single crystal nickel base superalloy

Abstract

By means of TEM observation and finite element analysis, an investigation has been made into the directional coarsening of the γ′ phase for a single crystal nickel base superalloy with [001] orientation during creep at 1040°C. The results show that the strain energy change related to the elastic strain is to be the driving force for γ′ rafting. The extruded strain of the lattice in the cuboidal γ′ interfaces results in a supersaturation of the elements Ta and Al of larger atomic radius. The extrusion or expansion strain in the lattice of the cuboidal γ′ planes may repel or trap these atoms to promote the directional growth of the γ′ phase into a needle-like raft structure along the direction parallel to the stress axis under an applied compression stress, or into a meshlike raft structure along the direction perpendicular to stress axis under applied tensile stress. The normal direction of the expanding lattice is supposed to be the one in which the γ′ rafts grow. The rate of γ′ rafting is enhanced by increasing viscoplastic flow in the γ matrix and elastic strain in the γ′ phase. Therefore, there is a smaller rate of growth under compressive than under tensile stress as a result of the smaller expansion strain and viscoplastic flow occurring in the former.     

Macroscopic theory and nonlinear finite element analysis of micromechanics of single crystals at finite strains

The present paper is concerned with an efficient framework for a nonlinear finite element procedure for the macroscopic rate-independent and rate-dependent analysis of micromechanics of metal single crystals undergoing finite elastic-plastic deformations which is based on the assumption that inelastic deformation is solely due to crystallographic slip. The formulation relies on a multiplicative decomposition of the material deformation gradient into incompressible elastic and plastic as well as a scalar valued volumetric part. Furthermore, the crystal deformation is described as arising from two distinct physical mechanisms, elastic deformation due to distortion of the lattice and crystallographic slip due to shearing along certain preferred lattice planes in certain preferred lattice directions. Macro- and microscopic stress measures are related to Green’s macroscopic strains via a hyperelastic constitutive law based on a free energy potential function, whereas plastic potentials expressed in terms of the generalized Schmid stress lead to a normality rule for the macroscopic plastic strain rate. Estimates of the microscopic stress and strain histories are obtained via a highly stable and very accurate semi-implicit scalar integration procedure which employs a plastic predictor followed by an elastic corrector step, and, furthermore, the development of a consistent elastic-plastic tangent operator as well as its implementation into a nonlinear finite element program will also be discussed. Finally, the numerical simulation of finite strain elastic-plastic tension tests is presented to demonstrate the efficiency of the algorithm.     

Finite element visualization of fatigue crack closure in plane stress and plane strain

Elastic-plastic finite element simulations of growing fatigue cracks in both plane stress and plane strain are used as an aid to visualization and analysis of the crack closure phenomenon. Residual stress and strain fields near the crack tip are depicted by both color fringe plots and x-y graphs. Development of the residual plastic stretch in the wake of a growing plane stress fatigue crack is shown to be associated with the transfer of material from the thickness direction to the axial direction. Finite element analyses indicate that crack closure does occur under pure plane strain conditions. The development of the residual plastic stretch in plane strain is shown to be associated with the transfer of material from the in-plane transverse direction to the axial direction. This in-plane contraction also leads to the generation of complex residual stress fields. The total length of closed crack at minimum load in plane strain is shown to be a small fraction of the total crack length, especially for positive stress ratios. This suggests that experimental measurement of plane strain closure would be extremely difficult, and may explain why some investigators have concluded that closure does not occur in plane strain.     

中低应变率下砂岩动力特性试验研究

为研究岩石在中低速冲击下的动力特性,利用MTS和落锤冲击试验系统进行了红砂岩准静态和动态单轴压缩试验,获得了10-2-101.7 s-1应变率范围砂岩全应力-应变曲线。结果表明,中低应变率加载条件下,砂岩经历典型压密、弹性变形、非稳定裂纹发展至脆性破裂后阶段。随着加载应变率的提高,砂岩峰值应力及其对应应变、残余应变均逐步增加,破坏模式则由X状共轭剪切破坏转变为劈裂破坏;动态强度增长遵循热活化和宏观黏性机制联合作用规律;中低应变率下岩石的吸收总能量和弹性应变能随变形演化规律基本一致,且弹性应变能和较耗散应变能的应变率效应更为显著。     

A thermo-micro-mechanical modeling for smart shape memory alloy woven composite under in-plane biaxial deformation

This paper presents a theoretical study of the in-plane behavior of Smart Shape Memory Alloy Woven Composites (SSMAWC) under biaxial loading by developing an integrated micromechanical constitutive model. The model studied in this research is established on the geometric parameters of fibers, metal layers, unit cell, the material constants of composite constituents, and the orientation of fibers, in which the fibers in one direction are SMA ones. The Helmholtz free energy of a Shape Memory Alloy, in 3-Dimensional and 1-Dimensional applications is derived. Using mechanical energy of matrix and elastic yarns, the constitutive relations are developed with the use of strain energy approach and energy variation theorem. The kinetic relations of SMA depicted by Brinson is coupled with the final governing equation of the composite to predict the stress history in smart shape memory alloy woven composites. The deflection of the structure, subjected to uniform biaxial loading is studied numerically. It is found that the effect of Shape Memory Effect (SME) of the SMA wires on the behavior of plain woven flexible fabric composite is significant.     

Measurement of Residual Stresses with Optical Techniques

Abstract:  The goal of this work was the development of other experimental techniques to measure residual stresses, as an alternative to the hole-drilling method with strain gauges. The proposed experimental techniques are based on the use of Moiré interferometry and in-plane electronic speckle pattern interferometry (ESPI). Both are field techniques allowing the assessment of in-plane displacements without contact and high resolution. Grating replication techniques were developed to record high-quality diffraction gratings onto the specimen's surfaces. An optical set-up of laser interferometry was developed to generate the master grating (virtual). An in-plane ESPI set-up was also designed and implemented to measure displacements in one direction. The stress relaxation was promoted by the blind hole-drilling and the obtained fringe patterns (Moiré and speckle) were video-recorded. Image processing techniques were applied to assess the in-plane strain field. A finite-element code ( ansys ®) was used to simulate the stress relaxation process, whose values were compared with the experimental data, and to calculate the hole-drilling calibration constants.     

Versatile analysis of limited plasticity by body force method

A problem of thermally induced residual stress under plane strain constraint is considered based on a body force method (BFM). As a numerical example, a simple problem of limited plasticity due to a uniform strength of transient line heat source of finite width, which is applied to a surface of a semi-infinite solid for a short duration of time, was considered. Although the out-of-plane component of normal stress (σ _zz ) can be simply estimated from the in-plane normal stress components σ _xx , σ _yy and the Poisson’s ratio ν as σ _zz  = ν(σ _xx  + σ _yy ) for elastic plane strain problems, this relation is violated when plasticity is considered. As a result, the residual stress in the direction of out-of-plane found to be a major component in the present problem.     

Wedge crack nucleation in Type 316 stainless steel

Type 316 austenitic steel has been heat-treated to produce a range of grain sizes and then creep-tested at 625° C at various stresses so as to examine the nucleation and the factors which effect the nucleation of grain-boundary triple point or wedge cracks. An internal marker technique was used to evaluate the extent of the grain-boundary sliding in relation to the total creep strain. Triple point crack nucleation occurred over the entire range of grain sizes and stresses examined when the product of the stress and grain-boundary displacement reached a critical value; the effective surface energy for grain boundary fracture, estimated using an expression derived by Stroh, was in approximate agreement with the surface free energy value indicating that only limited relaxation occurred by plastic deformation. The first cracks were observed to form along grain boundary facets perpendicular to the applied stress direction and with the sliding grain boundaries at high angles (60 to 80°) to the crack growth direction. Subsequent cracking occurred under conditions which deviated slightly from this initial condition, and the increase in crack density with strain was expressed in terms of geometrical factors which take account of the orientation effects.     

3004铝合金晶格和织构演化的原位X射线衍射研究

为探究3004铝合金板材在拉伸变形过程中晶粒取向变化和晶格应变行为,明确两者在塑性变形过程中的竞争机制和作用,本文首次将原位拉伸方法用于铝合金织构演化和晶格应变行为的研究中,利用试验装置对3004铝合金进行定量应变拉伸,并在不同变形量下对样品进行X射线衍射物相和织构测试分析.实验结果表明:样品在弹性变形区晶格常数随应变...     

A large deformation anisotropic thermoviscoplastic constitutive model

Summary An anisotropic large deformation thermoviscoplastic constitutive model has been formulated in which flow is regarded as a dissipative process characterized by a driving energy, a threshold energy, and a retardation time. Thermodynamic state functions such as internal energy are derived explicitly as functions of the state variables, namely temperature, elastic strain and flow strain. The model developed here is relevant to applications such as temperature rise and stress relaxation in metals under shock loading.     

Collapse of periodic planar lattices under uniaxial compression, part I: Quasi-static strength predicted by limit analysis

The collapse strength is analyzed for typical periodic planar lattices under uniaxial compression. In this part, the quasi-static strengths of the lattices are predicted by limit analysis, with the consideration of the elastic effect and large deformation effect. The planar lattices are firstly classified into bending-dominated and membrane-dominated structures. Collapse strength of typical bending-dominated lattices, such as hexagonal and rhombus structures, has identical initial lower bound and upper bound, so that the equivalent stress–strain curve of a bending-dominated lattice possesses a plateau. On the contrary, the equivalent stress–strain curve of a membrane-dominated lattice, such as square, triangular or Kagome structure, usually contains a peak followed by a sharp drop without a plateau. Consequently, the energy absorption behavior of the bending-dominated lattices is similar to type I structure, while that of the membrane-dominated lattices is similar to type II structure.     

Revisiting intrinsic brittleness and deformation behavior of B2 NiAl intermetallic compound: A first-principles study

For NiAl intermetallic compound with B2 structure, there is still no calculation combining models of single and multiple layers while using the same basic set. Furthermore, some recently proposed criteria for brittleness and toughness have not been used to analyze its deformation behavior. Thus, first-principles calculation was applied to comprehensively study the elastic properties, ideal strength, generalized stacking fault energy and surface energy of B2-NiAl intermetallic compound. The results suggest that calculations based on the current basic set give more accurate lattice parameters and elastic moduli. The Pugh criterion and Cauchy pressure cannot be used to interpret the intrinsic brittleness of NiAl. In comparison, the ductility parameter based on the strain energy under elastic instability and ZCT and Rice criteria based on generalized stacking fault energy and surface energy successfully identify the intrinsic brittleness of the NiAl intermetallic compound. The reason why [111] slip always occurs in the deformation along [100] direction was clarified by examining the critical value for brittle-ductile transition. The results of density of state indicate shear deformation has less impact on structural stability, and the change of charge density difference implies that <001> shear induces more intensive redistribution of charge density, which is well correlated to the brittleness and deformation behavior of NiAl intermetallic compound.     

Analytical beam theory for the in-plane deformation of a composite strip with in-plane curvature

The variational-asymptotic-method (VAM) provides a mathematically rigorous way to reduce a three-dimensional elasticity formulation to a one-dimensional beam theory without ad hoc assumptions. In this work, the VAM is employed to develop a beam theory to analyze the in-plane deformation of a laminated strip-beam with initial in-plane curvature. The cross-sectional stiffness constants and recovery relations for stress and strain are presented as analytical expressions. For the case of zero initial curvature, consistency of the expressions with those of plate theory is demonstrated. For strip-beams with initial curvature in the in-plane direction, results obtained show explicit dependence on the curvature. Results are verified by comparison with those obtained from VABS, the accuracy and consistency of which with three-dimensional finite elements has been reported in several published works. In addition to the internal consistency check this work provides and its utility in helping to validate VABS (which is based on the principles of VAM), it is hoped that the results obtained herein, since they are all analytical expressions, will help researchers and engineers validate the effect of initial curvature in their beam theories, whether existing or new.     

Measurement of the evolution of internal strain and load partitioning in magnesium hybrid composites under compression load using in-situ synchrotron X-ray diffraction analysis

Energy dispersive synchrotron X-ray diffraction analysis has been applied to evaluate the evolution of average internal elastic lattice strains under compression load within the phases of magnesium hybrid composites, reinforced by silicon-carbide particles and Saffil® alumina short fibres. This allows for the calculation of phase stresses and thus the load partitioning. The mean elastic misfit stresses were calculated using an Eshelby type modelling. Considering the external load, prediction of the phase-specific stresses for elastic composite deformation was performed and the results were compared to the experimental data obtained.Matrix elastic lattice strains reveal high plastic anisotropy due to the activation of different deformation modes in the form of crystallographic slip and mechanical twinning. The formation of twins, verified by diffraction intensity shifts due to crystallographic reorientation, was found to affect the sharing of load between the participating phases. Consequently different regimes of composite deformation were specified. This comprises elastic regions characterized by linear strain and stress growth for all phases as well as plastic regions showing nonlinear distributions.     

Stress and strain energy of a periodic array of interfacial wedge disclination dipoles in a transversely isotropic bicrystal

Analytical closed-form solutions are obtained for the elastic stress and strain energy density fields of a periodic array of interfacial wedge disclination dipoles in a bicrystal. The adjoining crystals are transversely isotropic with maximum dissimilar in-plane crystallographic orientations (0 and π/2). The solutions are obtained by the method of image dislocations. The strain energy per unit area of the bicrystal interface is also obtained numerically. The results show that significant discrepancies can exist between the bicrystal and the isotropic homogeneous solutions. The rates of decrease/increase of the strain energy density and stresses from the interface are smaller in the crystal whose larger stiffness direction is perpendicular to the interface. Also, the strain energy of the bicrystal boundary is a function of the dipole arm length (2a) and period (L). The maximum strain energy occurs at a/L=0.25 and is estimated to be ∼8.9 J/m² if the dipole period is 10 nm and the disclination strength is π/2.     

The effect of different forms of strain energy functions in hyperelasticity‐based crystal plasticity models on texture evolution and mechanical response of face‐centered cubic crystals

Micro‐mechanical and macro‐mechanical behavior of face‐centered cubic (FCC) crystals is investigated by using different forms of strain energy functions in hyperelastic material models in crystal plasticity finite element framework. A quadratic strain energy function with anisotropic elastic constants, a polyconvex strain energy function with invariants associated with the cubic symmetry, and a strain energy function from an inter‐atomic potential are considered in hyperelastic material models to describe the elastic deformation of FCC crystals. In our numerical experiments, the trajectories of {111} poles in the pole figure and the accumulated plastic slips of FCC coppers under uniaxial tension and simple shear depend on the choice of strain energy functions when the slip resistance of the slip systems is high. The ability of strain energy functions in this study to represent elastic lattice distortions in crystals varies with the amount of elastic deformation and the shape of deformed lattice. However, numerical results show that the change of macroscopic mechanical behavior of FCC coppers is not significant for the choice of strain energy functions, compared with the change of crystallographic texture evolution. Copyright © 2014 John Wiley & Sons, Ltd.