Elastic-plastic Field Research Articles

A predictive strain-gradient model with no undetermined constants or length scales

A general meso‑scale (GM) crystal plasticity (CP) model was developed that accounts for lower-order (strain hardening) and higher-order (internal stress) effects of geometrically necessary dislocations (GNDs). It is predictive: no arbitrary parameters or length scales were invoked and no ad hoc numerical techniques were employed. It uses general stress field equations for GND content and a novel harmonization technique to enforce consistency of elastic long-range singular defect fields with applied elastic-plastic fields. The model facilitates implementation in commercial finite element programs without requiring special elements, special boundary conditions, or access to element shape functions. GM simulations confirmed, with improved accuracy, previously published predictions of the Hall-Petch effect, Bauschinger effect, and anelasticity. Previously unpredicted phenomena were also predicted: anelasticity and hysteresis for single Ta crystals and strain-hardening stagnation. The internal stresses (higher-order effect) dominate at large length scales, while at small length scales, the GND density hardening (lower-order effect) dominates. GM predicts that strain heterogeneity and consequent GND internal stresses are important factors in anelasticity.

NEWLINE CSD composite steel-concrete folded slab bridge superstructure design program

Abstract The paper presents the calculation algorithm and one module of the Newline CSD (Composite Structure Design) railway bridge design program for the folded slab bridge superstructures with composite steel-concrete section. The calculation methods in the elastic-plastic field have been complied with the provisions of the European norms in force. In this respect, the theoretical principles regarding the calculations of the railway bridges, the usual materials for the construction of bridges with composite steel-concrete, simplified calculation assumptions of these sections, as well as the calculation in the elastic and plastic field are presented.

Quantification of the Influence of Residual Stresses on Fatigue Strength of Al-Alloy Welded Joints by Means of the Local Strain Energy Density Approach

Depending on boundary conditions, welding parameters and plate thickness, high residual tresses may arise near the weld toe of a welded joint. Compressive or tensile residual stresses significantly influence the fatigue strength of the joints in the high-cycle regime. If the weld toe is modelled as a sharp, zero-radius V-shaped notch, the residual stress fields can be expressed in terms of residual notch stress intensity factors (R–NSIFs) calculated in the elastic or elastic-plastic fields. The possibility to quantify the intensity of the residual singular stress field by means of the R–NSIFs allows the designer to estimate the influence of residual stresses on the fatigue life of welded joints. In this work, the influence of residual stresses on the fatigue resistance of Al-alloy butt-welded joints is estimated by using the local stain energy density approach. Values predicted by the proposed method show a good agreement with experimental data taken from literature.

Fatigue investigation at high load ratio R of a quenched and tempered chromium molybdenum steel

The fatigue behavior at high number of cycles in elastic-plastic field of quenched and tempered carbon chromium steel was experimentally investigated for high performance reciprocating compressors application. Fatigue tests on un-notched specimens were performed both under load and strain controls, by imposing different levels of stress/strain and for each of them different values of stress ratios R, especially high values. Stress and strain trends have been monitored, during the fatigue life, and either ratcheting or relaxation, respectively, was evident.The stress control tests have resulted into fatigue fractures only for low values of R with significant ratcheting and an increasing rate during the final part of the test, thus the fracture could be considered as a synergy between fatigue damage and plastic failure. On the contrary, the ratcheting stabilized for high values of R and the tests were finalized without any fracture. Within an intermediate region, for medium/high values of R, a minor ratcheting and the fracture transition have been found. Similarly, for the tests under strain control, low values of R showed fatigue fractures despite a considerable relaxation, conversely for high values of R, the relaxation was limited without any fracture. After reporting the tests on the Haigh plane, the Smith-Watson-Topper equation (SWT) provided the best prediction of the fatigue strength, at least until the intersection with the ultimate stress line, both under stress and strain control loadings. The cyclic behavior of the material was then investigated through several static and cyclic tests on plain specimens. A kinematic hardening Chaboche model, with three parameter couples, was proposed and the values of these parameters derived and discussed. Finally, other tests have been conducted on notched specimens with C geometry and blunt radius, again at high R values. FE analysis allowed the prediction of the stress evolution during the loading cycling, implementing the Chaboche model, and observing a combined effect of ratcheting and relaxation at the notch tip. The stabilized stresses were finally reported on the Haigh diagram and the results were found in agreement with the plain specimen fatigue line.

Analytical characterization of plastic flow in spot welded joints

An analytical procedure for the evaluation of the elastic–plastic behaviour of spot welded joints, in terms of global stiffness is presented in this paper. The analytical procedure is based on a new reference theoretical model of the sheet region close to spot welded joint able to follow the evolution of plastic flow close to the joint. The new closed-form solutions allow to define the deflection of spot joint when an axial load is applied and plasticization occurred. The reference theoretical model is based on theory of elasticity and consists in a circular plate having two annular portions with different variable thickness and having a central rigid core representing the spot weld. This model allows to correctly simulate the actual plasticization radius when load increases and the global stiffness of the actual joint.The analytical procedure presented is new and lead to the definition of a spot weld finite element, able to precisely evaluate both local and overall stiffness of spot joints, also in elastic plastic field. This spot weld element lead to accurate simulation of multi spot welded structures with a very low computational effort.

Element Bearing Ratio Based Shakedown Analysis for Branch Pipe

Shakedown analysis is important for branch pipe because it is often damaged under various water pressure. In this paper, an element bearing ratio (EBR) based shakedown analysis method is employed for shakedown analysis of branch pipe. The EBR is used to replace the stress term in classical optimization problem in the procedure, and series of residual EBR fields can be generated by the D-value of the elastic-plastic EBR fields and the elastic EBR fields at every incremental loading step. The shakedown load is determined by performing an incremental non-linear static analysis when the yield criterion is arrived either by the elastic-plastic EBR fields or residual EBR fields. By introducing the EBR, the proposed procedure can be easily used to shakedown analysis of branch pipe with multi-material and complicated configuration. Numerical examples validate the method and demonstrate its performance.

Side-groove effects in three-dimensional small-scale yielding: A load and thickness-scaling model

This study investigates the influence of side grooves on near-front fields that drive cleavage fracture processes in ferritic steels under 3D small-scale yielding conditions. High-fidelity, finite-strain analyses of boundary-layer models for initially straight crack fronts provide elastic–plastic fields. Numerical solutions demonstrate that non-dimensional, self-similar scaling of crack-front fields for plane-sided specimens also holds for the side-grooved configurations. Furthermore, Weibull stress values exhibit a non-dimensional, thickness scaling controlled by a single non-dimensional parameter. This thickness scaling holds for low-to-high hardening rates typical of ferritic steels under imposed loading levels that range in a 3D setting from near plane-strain to near plane-stress conditions.

OS0120 粒子分散複合材料のき裂先端近傍の弾性・弾塑性特異場に及ぼす粒子寸法とはく離損傷の影響

OS0120 粒子分散複合材料のき裂先端近傍の弾性・弾塑性特異場に及ぼす粒子寸法とはく離損傷の影響

Line field analysis and complex variable method for solving elastic-plastic fields around an anti-plane elliptic hole

A new approach is proposed to solve the elastic-plastic fields near the major-axis line of an elliptical hole. The complex variable method is used to determine the elastic fields near the major-axis line of the elliptical hole. Then, by using the line field analysis method, the exact and new solutions of the stresses, strains in the plastic zone, the size of the plastic region and the unit normal vector of the elastic-plastic boundary near the major-axis line of the elliptical hole are obtained for an anti-plane elliptical hole in a perfectly elastic-plastic solid. The usual small scale yielding assumptions are not adopted in the analysis. The present method is simple, easy and efficient. The influences of applied mechanical loading on the size of plastic zone are discussed.

Characterisation of crack tip stresses in elastic-perfectly plastic material under mode-I loading

Asymptotic crack tip stress fields are developed for a stationary plane strain crack in incompressible elastic-perfectly plastic material under mode-I loading. Detailed investigations have revealed that in between the two extreme conditions of crack tip constraint, that is, between the fully plastic Prandtl [1] field and the uniform stress field the most general elastic–plastic crack tip fields can be completely described by the 5-sector stress solution proposed in this article. The 3-sector stress field proposed by Li and Hancock [2] and the 4-sector field proposed by Zhu and Chao [3] are subsets of the general elastic–plastic field proposed in this work. This study has revealed that cases arise where the severe loss of crack tip constraint can lead to compressive yielding of crack flank. This particular situation leads to 5-sector stress field. Detailed studies have revealed that, in the most general case of elastic–plastic crack tip fields, the T π parameter proposed by Zhu and Chao [3] cannot be used as a constraint parameter to represent a unique state of stress at the crack tip. A new constraint-indexing parameter T CS-2 is proposed, which along with T p is capable of representing the entire elastic–plastic crack tip stress fields over all angles around a crack tip. Excellent agreement is obtained between the proposed asymptotic crack tip stress field and the full-field finite element results for constraint levels ranging from high to low. It is demonstrated that the proposed constraint parameters are adequate to represent the crack tip constraint arising due to specimen geometry and loading conditions as well as the additional constraint that arises due to weld strength mismatch.

T-stress effects on steady crack growth in a thin, ductile plate under small-scale yielding conditions: Three-dimensional modeling

The non-singular T-stress provides a first-order estimate of geometry and loading mode, e.g. tension vs. bending, effects on elastic–plastic, crack-front fields under mode I conditions. The T-stress has a pronounced effect on measured crack growth resistance curves for ductile metals – trends most computational models confirm using a two-dimensional setting. This work examines T-stress effects on three-dimensional (3D), elastic–plastic fields surrounding a steadily advancing crack for a moderately hardening material in the framework of a 3D, small-scale yielding boundary-layer model. A flat, straight crack front advances at a constant quasi-static rate under near invariant local and global mode I loading. The boundary-layer model has thickness B that defines the only geometric length-scale. The material flow properties and (local) toughness combine to limit the in-plane plastic-zone size during steady growth to at most a few multiples of the thickness (conditions obtainable, for example, in large, thin aluminum components). The computational model requires no crack growth criterion; rather, the crack front extends steadily at constant values of the plane-stress displacements imposed on the remote boundary for the specified far-field stress intensity factor and T-stress. The specific numerical results presented demonstrate similarity scaling of the 3D near-front stresses in terms of two non-dimensional loading parameters. The analyses reveal a strong effect of T-stress on key stress and strain quantities for low loading levels and less effect for higher loading levels, where much of the plastic zone experiences plane-stress conditions. To understand the combined effects of T-stress on stresses and plastic strain levels, normalized values from a simple void-growth model, computed over the crack plane for low loading, clearly reveal the tendency for crack-front tunneling, shear-lip formation near the outside surfaces, and a minimum steady-state fracture toughness for T = 0 loading.

Steady crack growth in a thin, ductile plate under small-scale yielding conditions: Three-dimensional modeling

Abstract This work employs high resolution, finite element computations to investigate key features of the elastic–plastic fields near a steadily advancing crack at quasi-static rates under three-dimensional, small-scale yielding conditions. The model represents a structurally thin component constructed of a material ( e.g ., Al and Ti alloys) with flow stress and fracture toughness properties that together limit the size of the in-plane plastic zone during steady-growth to no more than several multiples of the plate thickness. The computational approach generalizes the streamline integration procedure used previously for two-dimensional studies into three dimensions to represent steady-state growth on a fixed mesh in a boundary-layer framework. The plate thickness provides the only geometrical length scale. Crack extension occurs at the remotely applied, fixed loading without the need for a local growth criterion. In the first computations of this type, the present work considers a straight crack front advancing under local and global mode I loading with zero T -stress in a moderately hardening material. Applied remote loads at steady growth generate plastic zone sizes ahead of the advancing crack front ranging from 0.25 to 6.4 times the thickness. Key results include: (1) the crack-front fields exhibit a self-similar scaling characterized by a non-dimensional loading parameter; (2) three-dimensional effects extend to distances of approximately 1.5–2.5 times the thickness ahead of the advancing crack front for key values of this loading parameter, beyond which the fields (elastic–plastic then linear-elastic at greater distances) become uniform over the thickness; and (3) crack opening profiles on the outside surface reveal a “wedge-like”, opening shape which simplifies the definition of a crack-tip opening angle.

Fatigue Crack Growth Rate of 16mnr Steel with Effect of Stress Ratio

Fatigue crack growth was simulated by using a newly developed unified model on the fatigue initiation and crack growth based on an incremental multiaxial fatigue criterion. The cyclic elastic-plastic stress-strain field was analyzed using the general-purpose finite element software (ABAQUS) with the implementation of a robust cyclic plasticity theory. The fatigue crack growth rates with respect to three different stress ratios were selected as the benchmark to check the unified model. The predicted results agreed with the experimental data very well. The insensitivity of the crack growth rate to the stress ratio is due to the fast mean stress relaxation.

Elastic–plastic analysis of rotating disks having non-linearly variable thickness: residual stresses by overspeeding and service stress state reduction

Two models for evaluation of elastic and elastic–plastic stress and strain in non-linear variable thickness rotating disks, either solid or annular, subjected to such a rotational speed to determine stresses beyond yielding are presented. The first model regards the elastic field and the second concerns the elastic–plastic field, assuming that material hardening is isotropic and follows a most general hardening power-law. In the elastic region, a non-homogeneous hypergeometric differential equation is obtained. Such differential equation, which solves the elastic problem in closed form for non-linear variable thickness disks, with thickness given by the power of a linear function which may define a fourfold infinity of profiles, is integrated in closed form. As concerns the elastic–plastic analysis, first of all the introduction is made of a correlation between equivalent plastic strain and equivalent stress according to Von Mises, which is more general than those known from literature. In the case of isotropic hardening a second-order, non-homogeneous, non-linear differential equation is found, which governs the stress state in the plastic region of the disk. The procedure allows to calculate stress and displacement states in the two regions—plastic and elastic—of the disk subjected to prestressing by overspeeding. Several examples of disks, also prestressed by overspeeding, are considered (annular and solid, convex or concave, and linear tapered disks); the matching of results of the theoretical model and those obtained by means of FEA is very good. Lastly, the residual stress state can be found in a prestressed disk by overspeeding and the stress state in the actual operating condition in the same disk is evaluated.

Modeling of Fatigue Crack Growth Based on Two Cyclic Plasticity Models

Based on two different cyclic plasticity models, fatigue crack growth for 16MnR steel specimens is simulated by using the same multi-axial fatigue damage criterion. The first plasticity model is the Jiang and Sehitoglu model and the second plasticity model is the simple nonlinear kinematic hardening model. The elastic-plastic stress-strain field near the crack tip is obtained respectively by using the two plasticity models. According to the same fatigue criterion, different fatigue damage near the crack tip is determined on the basis of stress-strain responses. The first plasticity model can accurately capture cyclic plasticity deformation behavior and predictions of fatigue crack growth rate are in agreement with the experimental results. However, lots of material constants in the model need to be fitted and more experimental tests should be conducted. The second plasticity model is very simple. The parameters of the model can be acquired easily by uniaxial fatigue tests. Compared with experimental data, the prediction results of fatigue crack growth rate lead to some errors by adopting the second plasticity model.

An analytical and computational study of crack initiation under transient creep conditions

An analytical method has been developed to predict creep crack initiation (CCI), based on the accumulation of a critical level of damage at a critical distance. The method accounts for the re-distribution of stress from the elastic or elastic–plastic field, experienced on initial loading, to a steady state creep stress distribution, via a transient creep region. The method has been applied to predict CCI times in a fracture specimen of type 316H stainless steel at 550 °C. The failure model has been also been implemented into a finite element (FE) framework. Reasonable and conservative predictions of CCI time can be obtained from the analytical solution relative to FE solutions. Conservative predictions of experimental CCI times are obtained when stress redistribution is taking into account. However, CCI times predicted from a steady state creep model are found to be non-conservative.

General form of matching equation of elastic-plastic field near crack line for mode I crack under plane stress condition

Crack line field analysis method has become an independent method for crack elastic-plastic analysis, which greatly simplifies the complexity of crack elastic-plastic problems and overcomes the corresponding mathematical difficulty. With this method, the precise elastic-plastic solutions near crack lines for variety of crack problems can be obtained. But up to now all solutions obtained by this method were for different concrete problems, no general steps and no general form of matching equations near crack line are given out. With crack line analysis method, this paper proposes the general steps of elastic-plastic analysis near crack line for mode I crack in elastic-perfectly plastic solids under plane stress condition, and in turn given out the solving process and result for a specific problem.

Elastic and elastic–plastic fields on circular rings containing a V-notch under inclined loads

Elastic and elastic–plastic finite element analyses are described for circular rings containing a V-notch on the internal radius. The circular rings are subjected to a pair of compressive loads at different angles to the plane of the notch axis. In the elastic analysis, the mixed-mode stress field near the notch root is calculated for a sharp tip V-notch with or without a short precrack. The analyses include calculations of the stress intensity factors of mode I and mode II, and of the energy release rate for crack extension. In the elastic–plastic analysis, the stress distribution near the notch root is presented. The relationship between the notch root radius and the plastic zone is described. The influence of the angle of loading on the distribution of elastic–plastic stresses is discussed. In order to justify the results of the elastic–plastic numerical method, a test of constant loading with a stainless steel specimen is carried out by using a Moiré interferometry method. Furthermore, 10 tests of crack initiation by cyclic and inclined loading are performed to examine the adaptation of the finite element analysis to the experiments. The results of the calculation are found to correspond to the experimental data.

A Hybrid Moire-Interferometry and Finite-Element Method Based on a Variational Principle Minimizing Experimental Measurement Errors. Case of Elastic-Plastic Deformation Field.

In a previous study, for the case of elastic deformation field, the authors have developed a hybrid experimental-numerical method based on a variational principle minimizing experimental measurement errors. In this stydy, for the case of elastic-plastic deformation field, first, an incremental variational principle is derived to minimize the errors associated with a full-field displacement measurement such as moire interferometry. Next, on the basis of this variational principle, a new hybrid moire-interferometry and finite element method is developed for the case of elastic-plastic deformation field. The present hybrid method demonstrates automatic detection and elimination of the measurement errors and smooth visualization of stress and strain contours. Furthermore, the present hybrid method automatically achieves the path independence of the T* integral, restoring the path-dependence caused by the measurement errors. This paper provides the foundation of an intelligent measurement and visualization of displacement and stress fields in actual structural components.

Limitations to leading-order asymptotic solutions for ELASTIC–PLASTIC crack growth

Previous work has shown that there are significant discrepancies between leading-order asymptotic analytical solutions for the elastic–plastic fields near growing crack tips and detailed numerical finite element solutions of the same problems. The evidence is clearest in the simplest physically realistic case : quasi-static anti-plane shear crack growth in homogeneous, isotropic elastic–ideally plastic material. There, the sole extant asymptotic analytical solution involves a plastic loading sector of radial stress characteristics extending about 20° from ahead of the crack, followed by elastic unloading, whereas detailed numerical finite element solutions show the presence of an additional sector of plastic loading, extending from about 20 to about 50°, that is comprised of non-radial characteristics. To explore how the asymptotic analysis can completely miss this important solution feature, we derive an exact representation for the stress and deformation fields in such a propagating region of non-radial characteristics, as well as in the other allowable solution regions. These exact solutions contain arbitrary functions, which are determined by applying asymptotic analysis to the solutions and assembling a complete near-tip solution, valid through second order, that is in agreement with the numerical finite element results. In so doing, we prove that the angular extent of the sector of non-radial characteristics, while substantial until extremely close to the crack tip, vanishes in the limit as the tip is approached, and that the solution in this sector is not of variable–separable form. Beyond resolving the analytical–numerical discrepancies in this specific anti-plane shear problem, the analysis serves to caution, by explicit example, that purely leading-order asymptotic solutions to nonlinear crack growth problems cannot in general capture all essential physical features of the near-tip fields, and that the often-invoked assumption of variable–separable solutions is not always valid.