Buckling deformation in axially compressed elastic-plastic cylindrical shells initiated by local axisymmetric imperfections

Summary A solution for growth of a perturbation describing buckling deformation initiated by a local axisymmetric imperfection in an axially compressed elastic-plastic cylindrical shell is obtained in simple closed form for small time. The constitutive relations for the plastic strains are based on simple J ₂ flow theory. A comparison is made with bifurcation analysis, and localization of the buckling deformation is examined.     

Microscopic observation of voids and transverse crack initiation in CFRP laminates

In situ three-point bending tests under observation using scanning electron microscopy were performed for specimens including voids to investigate the effect of voids on transverse crack initiation in carbon fiber-reinforced plastic (CFRP) laminates. First, initial failure load (i.e. applied load at the first transverse crack initiation) was investigated. Microscopic strain distributions were then measured by digital image correlation analysis using SEM pictures taken before and during loading in the in situ tests. In addition, specimens including voids and transverse cracks after the in situ tests were observed using X-ray computed tomography to clarify transverse crack onset locations with respect to void shapes and distributions. These experiment results suggested that voids actually caused strain concentration and corresponding local plastic deformation, and finally resulted in reduction of macroscopic initial failure strains in CFRP laminates.     

Analysis of the Results of Mechanical Testing of Metals by Constructing the Diagrams of Structural States

For polycrystalline metals and alloys with bcc (Mo, Fe, and Fe–Si) and fcc (Ni and Cu) crystal lattices, it is shown that the application of the method of reconstruction of parabolic stress–strain diagrams on S –eⁿcoordinates, where S and e are the actual stress and strain, respectively, and n is the strain-hardening index, makes it possible to represent the results of mechanical testing in the form of a diagram of structural states plotted in the form of the dependences of actual stresses and strains on temperature. This diagram practically completely describes the changes in the strength and plastic characteristics of the materials and their structural states in the process of plastic deformation. We study specific features of the construction of these diagrams depending on the composition of the alloy, its structural state, the energy of stacking faults, etc. On the basis of the analysis of the character of correlations between the critical values of strains and stresses and the mechanisms of plastic deformation within broad ranges of temperature and structural states, we discuss the possibilities of scientific and practical application of the diagrams of actual stresses and strains vs temperature.     

Formulation and numerical treatment of incompressibility constraints in large strain elastic–plastic analysis

The present paper is concerned with an efficient framework for a nonlinear finite element procedure for the rate‐independent finite strain analysis of solids undergoing large elastic‐isochoric plastic deformations. The formulation relies on the introduction of a mixed‐variant metric deformation tensor which will be multiplicatively decomposed into a plastic and an elastic part. This leads to the definition of an appropriate logarithmic strain measure which can be additively decomposed into the exact isochoric (deviatoric) and volumetric (spheric) strain measures. This fact may be seen as the basic idea in the formulation of appropriate mixed finite elements which guarantee the accurate computation of isochoric strains. The mixed‐variant logarithmic elastic strain tensor provides a basis for the definition of a local isotropic hyperelastic stress response whereas the plastic material behavior is assumed to be governed by a generalized J₂ yield criterion and rate‐independent isochoric plastic strain rates are computed using an associated flow rule. On the numerical side, the computation of the logarithmic strain tensors is based on higher‐order Padé approximations. To be able to take into account the plastic incompressibility constraint a modified mixed variational principle is considered which leads to a quasi‐displacement finite element procedure. Finally, the numerical solution of finite strain elastic‐plastic problems is presented to demonstrate the efficiency and the accuracy of the algorithm. Copyright © 1999 John Wiley & Sons, Ltd.     

Macro‐ and Nanomechanical Properties and Strain Rate Sensitivity of Accumulative Roll Bonded and Equal Channel Angular Pressed Ultrafine‐Grained Materials

Several processes of severe plastic deformation are suitable for the production of materials with ultrafine‐grained microstructures which are known to exhibit high strength and often good ductility as well as strain rate sensitive behavior. The most promising ones are equal channel angular pressing (ECAP) for bulk material and accumulative roll bonding (ARB) for the production of sheet material. In order to evaluate the influence of the process on these mechanical properties and the strain rate sensitivity, tensile tests, and nanoindentation tests were performed on material produced up to similar effective plastic strains of ε_ARB = 6.4 and ε_ECAP = 6.3. It could be shown that the macroscopic strength is slightly higher for ARB than for ECAP material and vice versa in nanoindentation. Independent of the testing method, the strain rate sensitivities and activation volumes are similar for both materials. Thus, both processes performed up to similar effective plastic strains lead to comparable improvements in the mechanical properties. Additionally it could be shown, that this comparison allows the identification of the dominant deformation mechanism which is responsible for the observed strain rate sensitivity.     

Microstructural evolution over a large strain range in aluminium deformed by cyclic-extrusion–compression

Polycrystalline pure aluminium (99.99%) has been deformed at room temperature by the Cyclic-Extrusion–Compression (CEC)-method to strains in the range 0.9–60 (1–67 cycles). At different strains, the microstructure and local crystallography have been characterised in particular by transmission electron microscopy. It has been found that the microstructure develops from a cell block structure into an almost equiaxed structure of cells and subgrains, that the spacing between the boundaries subdividing the structure is almost unaffected by the strain and that the misorientation across these boundaries increases with the strain over the whole strain range. At the largest strain, the average misorientation across the deformation induced boundaries is 25°. The flow stress in compression is measured after the cyclic deformation and it is found that the flow stress increases with strain towards a saturation level which is reached at a relatively low strain. The discussion comprises the effect of deformation mode and plastic strain over a large strain range on the microstructural evolution and mechanical behaviour of aluminium.     

Role of geometry in plastic instability and fracture of tubes and sheet

Conditions for plastic instability and fracture for biaxially loaded tubes are compared to those for a sheet to assess the role of geometry. Thin-walled tubes of 70-30 brass were loaded in combined axial tension-internal pressure. The strains for diffuse instability, local instability and fracture were measured and compared to results on brass sheet. Uniform deformation (up to diffuse instability) was found to be very sensitive to geometry in agreement with theory. The uniform strain in tubes for axial plane strain is twice that for hoop plane strain and the uniform strain in tubes for balanced biaxial tension is only one third of that for sheet. The strain levels for local instability and fracture did not depend on geometry. No significant differences were found for axial vs. hoop loading in tubes and the critical strain levels for tubes were actually somewhat greater than those for sheet. Although the critical local strains are similar, the amount of useful (genera) deformation beyond diffuse instability for tubes is very limited because localization occurs rapidly. In bulged or punched sheet the geometry is stable and localization occurs gradually, providing significant post-uniform deformation.     

Tensile properties and inhomogeneous deformation of ferrite-martensite dual-phase steels

The tensile properties and inhomogeneous deformation of coarse ferrite-martensite dual-phase steels containing 17–50% martensite were analysed. The stress of dual-phase steels at equal strain increased with increasing volume fraction of martensite, f, but the rate of increase was reduced after f=0.3. The strain hardening rate was dependent on f at small strains ( 0.03), however, it became independent of f at larger strains. It was found that the deformation of the dual-phase steels divided into three different stages when f was less than about 0.3. The concurrent in situ stress-strain states of ferrite, martensite and their composite, and the stress ratios and strain ratios between ferrite and martensite were evaluated by means of a new stress and strain partition theory. The martensite phase deformed plastically after the uniform strain for f < 0.25, while it was plastic before the uniform strain for f > 0.25. The theoretical analyses for inhomogeneous deformation implied that the volume-fraction dependence of the stress and the characteristics of the strain-hardening rate were influenced by the plastic deformation of martensite. Further, the in situ stress-strain curves of ferrite and martensite and the internal stresses at respective phases were calculated from the partitioned stresses and strains.     

Internal friction in copper and α-brasses during plastic deformation

The internal friction Q ^–1 of annealed copper and -brass wires containing 10, 20, 30 and 35 at. % of zinc was studied by a torsional oscillation method during plastic deformation. The results are interpreted in terms of two theoretical models ascribing the amplitude-dependent internal friction, observed in the pre-yield stage, to coupling of the cyclic stress with the creep component of the deformation, and the amplitude-independent internal friction at larger, plastic, strains to losses arising from contributions of the torsional stress to the plastic deformation. Up to the maximum tensile strain of 1 % used in the experiments, the influence of zinc content on Q ^–1 is not pronounced.     

Studies on the stress-strain relations of dual-phase steels

The correlations of the work-hardening exponent,n, with quenching temperature, martensite volume-fraction (MVF) and solute concentration in ferrite are discussed and derived for dual-phase steel. The flow stress of dual-phase steel at low strain is suggested to be expressed by the combination of the terms due to plastic deformation in ferrite and elastic deformation of martensite. Previous experimental results are compared with the behaviour suggested by this theoretical work. In addition, an expression for the work hardening exponents at moderate strains and at the onset of necking are also theoretically suggested.     

Fully plastic crack-tip fields for plane strain shallow-cracked specimens under pure bending

Detailed finite element (PE) analyses are performed to study the effect of crack depth on crack-tip constraint at full yielding for pure bending of plane strain single-edge-cracked specimens. Analyses are based on small-strain formulations and perfect plasticity. The crack depth a/W ranges from 0.1 to 0.7, and the deformation is applied up to the limiting state of full plasticity where crack-tip stresses reach steady-state limiting values.At load levels smaller than the limit load (contained yielding), the crack-tip constraint (stress triaxiality) gradually decreases as a/W decreases, but, at load levels close to the limit load (or at the limit load), it decreases very sharply. In terms of a/W, tractable closed-form approximations for fully plastic crack-tip stress and strain fields are proposed, and fully plastic values of crack-tip stresses are re-phrased in terms of the Q-parameter [1, 2]. The role of crack-tip strains on fracture of shallow-cracked bending specimens is briefly discussed.     

Non-Uniform Distribution of Energy Density Near a Crack Tip in the Framework of HRR Model

The energy density distribution in the frame work of HRR model (Hutchinson, 1968a; Rice and Rosengren, 1968) is obtained. The analysis indicates that within a sector ahead of a crack, the hydrostatic stresses are very high while the effective stresses are very small, near to the yield stress, so the elastic strain energy density of volume deformation prevails in the forward sector. However, this sector is nearly a "rigid area" in HRR field (Hutchinson, 1968b). Meanwhile, a large amount of plastic dissipation distributes out of the sector, where the plastic dissipation makes up the main part of the J value. The high constraint means that the high elastic volume energy is stored in the local sector, thus the one-parameter fracture criterion based on J is invalid.     

The stressed state of a broad strip in uniaxial tension

The character of the stressed state of a broad strip in uniaxial tension in relation to the load level is investigated. Using 60 and 65G carbon steels as an example it is shown that in the material of the strip in the area of elastoplastic strains together with the longitudinal stress there is a purely transverse one which occurs with a plastic tensile deformation of about 2–3%. The transverse stress depends upon the level of plastic deformation and with an increase in the latter it increases. In this case the loading is complex and its trajectory has the form of a curve.Translated from Problemy Prochnosti, No. 8, pp. 48–51, August, 1995.     

SEM/EBSD based in situ studies of deformation induced phase transformations in supermartensitic stainless steels

Abstract

Recent year's equipment design has enabled the combination of in situ deformation tests with near real time electron backscatter diffraction (EBSD) mapping of the microstructure evolution in the scanning electron microscope (SEM). The present work involves studies of deformation induced phase transformations in supermartensitic steel containing ～40 vol.-% retained austenite at room temperature. The martensite formation was initiated already at low strains, and increased gradually with increasing plastic strains up to ～10%. It was observed that the martensite formed homogeneously within the microstructure, independent of the crystallographic orientations of the retained austenite. But no new martensite variants, besides those already present in the as received condition, did form during deformation. At the same time, the mutual distribution of these variants remained approximately constant throughout the deformation process.     

Large elastoplastic strains and the stressed state of a deformable gasket in high pressure equipment with diamond anvils

A procedure is developed and realized in the form of a numerical modelling program for deformation of a gasket in diamond anvils taking account of the effect of high pressure and large elastoplastic strains for the material. The procedure is based on the finite element method with a stepwise iteration algorithm (the initial stress method). In the case of considerable distortion of the finite element network with large strains a procedure is used for redefining the network deformation. A package of programs for solving elastoplastic problems with large strains and high pressure developed at the Institute of Superhard Materials of the Ukrainian National Academy of Sciences is used in the calculations. Two materials are considered: hardened stainless steel T301 and pressed lithographic limestone (PLL). A degree of compression of a factor of eight is achieved for PLL (Odquist parameter q5.5, elastic volumetric strain (EVS) 0.7, pressure 24 GPa) and a factor of 5.8 for steel T301 (q3, EVS 0.7, pressure 50 GPa). The distribution of elastic and plastic zones during deformation and stress distribution over the anvil-gasket contact surface are obtained, and the stagewise nature of the deformation process is revealed.Translated from Problemy Prochnosti, No. 3, pp. 78–87, March, 1996.     

钢箱梁爆炸冲击局部破坏的数值模拟

运用LS-DYNA非线性有限元软件,采用ALE多物质流-固耦合算法,研究了汽车炸弹（TNT当量100-500kg）桥面爆炸冲击作用下钢箱梁的局部破坏。结果表明,钢箱梁局部破坏模式有两种：（1）桥面板和底板均破口;（2）桥面板破口,底板产生局部塑性大变形。隔板的主要破坏模式为弯曲塑性大变形和破口。破坏参数随炸药当量的增加呈非线性增加。箱体内冲击波对底板、隔板的冲击作用相对较小,顶板破片的冲击作用是底板和隔板产生局部塑性大变形和破口的主要原因。     

Modelling surface ridging in ferritic stainless steel

Abstract

A new model is proposed to account for the occurrence of surface ridging (parallel corrugations) in ferritic stainless steel. In the absence of notable texture component clustering, it is shown that local anisotropy in plastic behaviour can still occur on a scale considerably larger than the grain size. The construction of a simple finite element model incorporating plasticity data from microtexture measurements demonstrates that parallel surface corrugations can be simulated during uniaxial tensile straining. It is shown that the corrugation profile is the result of the superimposition of a number of differential transverse strains that contribute to the overall deformation induced bending.     

A full tangent stiffness field-boundary-element formulation for geometric and material non-linear problems of solid mechanics

The field-boundary-element method naturally admits the solution algorithm in the incompressible regimes of fully developed plastic flow. This is not the case with the generally popular finite-element method, without further modifications to the method such as reduced integration or a mixed method for treating the dilatational deformation. The analyses by the field-boundary-element method for geometric and material non-linear problems are generally carried out by an incremental algorithm, where the velocities (or displacement increments) on the boundary are treated as the primary variables and an initial strain iteration method is commonly used to obtain the state of equilibrium. For problems such as buckling and diffused tensile necking, involving very large strains, such a solution scheme may not be able to capture the bifurcation phenomena, or the convergence will be unacceptably slow when the post-bifurcation behaviour needs to be analysed. To avoid this predicament, a full tangent stiffness field-boundary-element formulation which takes the initial stress–velocity gradient (displacement gradient) coupling terms accurately into account is presented in this paper. Here, the velocity field both inside and on the boundary are treated as primary variables. The large strain plasticity constitutive equation employed is based on an endochronic model of combined isotropic/kinematic hardening plasticity using the concepts of material director triad and the associated plastic spin. A generalized mid-point radial return algorithm is presented for determining the objective increments of stress from the computed velocity gradients. Numerical results are presented for problems of diffuse necking, involving very large strains and plastic instability, in initially perfect elastic–plastic plates under tension. These results demonstrate the clear superiority of the full tangent stiffness algorithm over the initial strain algorithm, in the context of the integral equation formulations for large strain plasticity.     

Plastic deformation — its role in fatigue crack propagation

Recognizing the fact that the effective driving force (ΔK _eff) determines the fatigue crack propagation (FCP) rate and that the shear strain, which is considered to develop due to an occurrence of crack closure, primarily contributes to the plastic deformation, an effort is made here to elucidate the role of plastic deformation in FCP by developing a correlation between the ΔK _eff and the applied driving force (ΔK) with shear strain as variable. The effect of the degree of plastic deformation (i.e. shear strain level) on the FCP rates at higher values of ΔK, where ΔK _eff approaches ΔK, approaching the Paris regime, appears minimal. On the other hand, the disparity between ΔK _eff and ΔK, which apparently increases with shear strain level, persists at lower values of ΔK. This suggests a strong influence of the degree of localized deformation on the FCP rates in the near threshold level. Hence, an improvement of FCP rates in the near threshold level should follow an effort that promotes the plastic deformation near the crack tip to a greater degree. This approach could, therefore, form the basis to explain the effect of the grain size, microstructure, environment,R-ratio and crack size on the near-threshold FCP rates.