Elastic-plastic Regime Research Articles

On the structural integrity assessment of elastic–plastic redundant cracked structures

The methods currently used for the assessment of the structural integrity of cracked structures do not consider, for the evaluation of the stresses acting on the flawed sections, the singularity introduced by the presence of the cracks. The effect of this presence is more pronounced in structures constituted of ductile materials, that behave in the elastic–plastic regime, because they are able to sustain a significant crack propagation before fracture. The formulation provided by the so-called “simplified procedures for the evaluation of cracked structures” allows the designer to consider the existence of cracks in the integrity assessments. The work herein presented, which is the follow-up of a previous one that defines the methodology to be applied taking into account the crack presence [Gorrochategui I. Comportamiento en Rotura de Tuberías de Alta Tenacidad con Sustentación Hiperestática en Régimen Elastoplástico, Tesis Doctoral, Escuela Técnica Superior de Ingenieros de Caminos, Canales y Puertos, Universidad de Cantabria, Diciembre 1993, Gorrochategui I, Gutiérrez-Solana F. A method for the assessment of hypersyatic cracked structures in the elastic–plastic regime, Engng Fract Mech 1998;61:519–35, Gorrochategui I, Gutiérrez-Solana F, González JJ, Varona JM. An extension of the application of elastic–plastic assessment to cracked pipework systems. Nucl Engng Des 1998;182:141–7], illustrates the way to perform this type of evaluation through the resolution of a realistic example. After a review of the currently existing “simplified procedures”, the Engineering Treatment Model (ETM) [Schwalbe K-H, Zerbst U, Kim Y-J, Brocks W, Cornec A, Heerens J, et al. The ETM Method for Assessing the Significance of Crack-Like Defects in Engineering Structures, Comprising the Versions ETM 97/1 and ETM 97/2. GKSS- Forschungszentrum Geesthacht GmbH, 1998] has been selected for this application and its selection is justified. The results of these calculations show the benefits obtained in the estimation of the maximum load bearing capacity of cracked structures if the existence of the flaws is considered.

Plasticity of multiscale nanofilamentary Cu∕Nb composite wires during in situ neutron diffraction: Codeformation and size effect

In situ neutron diffraction was performed on Cu∕Nb nanocomposite wires composed of a multiscale Cu matrix embedding Nb nanofilaments with a diameter of 267nm and spacing of 45nm. The evolution of elastic strains and peak profiles versus applied stress evidenced the codeformation behavior with different elastic-plastic regimes: the Cu matrix exhibit size effect in the finest channels while the Nb nanowhiskers remain elastic up to the macroscopic failure, with a strong load transfer from the Cu matrix onto the Nb filaments. The measured yield stress in the finest Cu channels is in agreement with calculations based on a single dislocation regime.

Microstructural effects in modeling the flow behavior of single-crystal superalloys

The deformation behavior of a [001]-oriented single-crystal superalloy (CMSX-4) having a high volume fraction of regularly arrayed cuboidal γ′ precipitates was simulated using a strain-gradient-dependent plasticity description for the γ matrix and an anisotropic elasticity description for the γ′ precipitate. A unit-cell mesh was adopted to represent the γ/γ′ microstructure. Numerical studies focused on clarification of the cause of the tension-compression (T-C) asymmetry in single-crystal superalloys. The numerical results suggest that the deformation-constraint effect induced by the γ/γ′ geometry gives rise to a T-C asymmetry that is different in both sign and magnitude for the elastic-plastic transition regime and the fully plastic regime.

Size Effect in the Plasticity of Multiscale Nanofilamentary Cu/Nb Composite Wires During in-situ Tensile Tests Under Neutron Beam

AbstractCopper-based high strength nanofilamentary wires reinforced by bcc nanofilaments (Nb or Ta) are prepared by severe plastic deformation for the winding of high pulsed magnets. In-situ tensile tests under neutron beam were performed on a Cu/Nb nanocomposite composed of a multiscale Cu matrix embedding 554 Nb filaments with a diameter of 267 nm and spacing of 45 nm. The evolution of elastic strains for individual lattice plane in each phase and peak profiles in the copper matrix versus applied stress evidenced the co-deformation behavior with different elastic-plastic regimes and load sharing: the Cu matrix exhibits size effect in the finest channels while the Nb nanowhiskers remain elastic up to the macroscopic failure, with a strong load transfer from the copper matrix onto zones that are still in the elastic regime. Taking into account results from residual lattice strains also determined by neutron diffraction, the yield stress in the finest Cu channels is in agreement with calculations based on a single dislocation regime.

Evaluation of the stress–strain curve of metallic materials by spherical indentation

A method for deducing the stress–strain uniaxial properties of metallic materials from instrumented spherical indentation is presented along with an experimental verification. An extensive finite element parametric analysis of the spherical indentation was performed in order to generate a database of load vs. depth of penetration curves for classes of materials selected in order to represent the metals commonly employed in structural applications. The stress–strain curves of the materials were represented with three parameters: the Young modulus for the elastic regime, the stress of proportionality limit and the strain-hardening coefficient for the elastic–plastic regime. The indentation curves simulated by the finite element analyses were fitted in order to obtain a continuous function which can produce accurate load vs. depth curves for any combination of the constitutive elastic–plastic parameters. On the basis of this continuous function, an optimization algorithm was then employed to deduce the material elastic–plastic parameters and the related stress–strain curve when the measured load vs. depth curve is available by an instrumented spherical indentation test. The proposed method was verified by comparing the predicted stress–strain curves with those directly measured for several metallic alloys having different mechanical properties. This result confirms the possibility to deduce the complete stress–strain curve of a metal alloy with good accuracy by a properly conducted instrumented spherical indentation test and a suitable interpretation technique of the measured quantities.

Tearing–fatigue interactions in 316L(N) austenitic stainless steel

This paper presents the results from a programme of tearing, fatigue and tearing–fatigue tests performed on specimens from a 316L(N) stainless steel plate. All tests were carried out at ambient temperature. The experimental results have been compared with assessments performed using current guidance within the R6 defect assessment method. The work has shown that there is some evidence that fatigue cycling modifies the JR-curve behaviour of this material. In most cases, the data lie approximately 20–30% above the base-line JR-curve. However, whilst there may be a modest influence of fatigue crack growth on the ductile tearing characteristics, it is difficult to separate this from experimental scatter. In tearing–fatigue tests performed at a stress ratio, R=0.2, ductile tearing reduces the fatigue crack growth rates by up to 50%. This is likely to result from the presence of a residual compressive zone at the crack-tip, and increased crack closure due to the irregular and non-matching fracture surfaces generated by the ductile crack growth mechanisms. For R=0.1 tearing–fatigue tests, fatigue crack growth rates are apparently enhanced by a factor up to of 10, particularly during the latter stages of the tests when Δ K>60 MPam. This is likely to result from: (i) loading being in the elastic–plastic regime where the J-integral (rather than K) characterises the crack-tip fields, (ii) increments of ductile tearing which may occur during each fatigue cycle, and (iii) crack blunting which reduces crack closure effects. For the R=0.2 tearing–fatigue tests, the linear summation approach described in R6 provides a consistently conservative prediction of ductile, fatigue and total crack growth during the tests. However, for the R=0.1 tearing–fatigue tests, the Paris law under-predicts fatigue crack growth rates. This may be corrected by using the Kaiser equation, which acknowledges loading in the elastic–plastic regime and incorporates incremental growth due to tearing as well as fatigue. R6 provides conservative predictions of instability for the CT specimen geometry tested in the current programme, both in terms of the critical crack growth and load required for instability to occur.

Tension-Compression Asymmetry in Plasticity Modeling of a Single Crystal Superalloy Using a "Unit Cell" Approach

The [001] tensile and compressive flow behavior of a single crystal superalloy CMSX-4 was simulated using a “unit-cell” mesh to represent the γ/γ′ microstructure. The simulation results showed a tension-compression (T-C) asymmetry, where the magnitude of the flow stress is larger in the elastic-plastic transition regime in tension, and is larger in compression in the plastic (flow softening) regime. The T-C flow behavior was related to the flow response of the γ-phase matrix under the geometric and kinematic constraint of the γ/γ′ unit cell.

Evaluation of the Effect of Crack Tip Constraint on Fatigue Crack Growth Rate in Inconel 718

Abstract The objective of this work has been to characterize the fatigue crack growth rate of Inconel 718 in the elastic and elastic-plastic regimes. The major new contribution here is to develop fatigue crack growth rate data on this alloy using shallow crack specimens subjected to cyclic loadings that involve material plasticity exceeding what is allowed by the standard Linear Elastic Fracture Mechanics (LEFM) procedures of ASTM E 647. Compact (C(T)) and three point bend (SE(B)) specimen geometries were used in this investigation. The SE(B) specimens were used to obtain shallow crack data using crack to depth ratios (a/W) as small as 0.08 in standard bend specimens with W = 50.8 mm. Compliance methods were used to estimate the crack length during the cyclic testing. The C(T) specimens were used to investigate the effect of fully reversed loading, i.e., R = −1.0. These specimens were tested only in deep crack configurations with a/W > 0.3. Both C(T) and SE(B) specimens were used to obtain high cycle fatigue crack growth data as well as some component of the low cycle fatigue crack growth rate data. The cyclic elastic stress intensity range was used to characterize the crack growth driving “force” in the high cycle regime as defined in ASTM E 647. A cyclic J integral range, as originally utilized by Dowling and Begley [1], was used in the elastic-plastic regime. High cycle and low cycle fatigue crack growth data were successfully obtained from tests on shallow crack SE(B) specimens. High cycle fatigue crack growth was not affected by specimen geometry or by crack length ratio, even for a/W ratios as low as 0.08. The low cycle fatigue crack growth rate was similar, but not identical, to what one would get by extrapolating the high cycle fatigue crack growth rate, as proposed by Dowling and Begley [1]. Under conditions of increasing J range, the crack growth rate under elastic-plastic conditions was accelerated, while under decreasing J range conditions the crack growth rate was decelerated in comparison to the extrapolated high cycle fatigue crack growth rate measurements. The R ratio did not affect the crack growth rate for the two cases tested here, namely R = 0.1 and R = −1.0. More rapidly increasing J range conditions resulted in greater crack growth rate acceleration. In the elastic-plastic fatigue regime, shallow crack specimens demonstrated slower crack growth rates than deep crack specimens.

Pore pressure tension cut off in two-phase finite element analyses

In the coupled finite element analysis of the two-phase, saturated soils the pore pressure could decrease below the atmospheric pressure in particular when the plastic dilation of the skeleton is accounted for. The consequent reduction of the bulk modulus of the liquid phase is here modelled in a simplified manner through a tension cut off on the pore pressure. Two alternative approaches are outlined in the framework of the finite element method. The first one introduces a unilateral constraint on the nodal pore pressures and involves manipulations on matrices of the assembled mesh, whilst the second approach requires calculations solely at the element level. The effects of the pore pressure tension cut off are illustrated through some undrained test examples in elastic–plastic regime.

Ultimate Strength of Aluminum Plates and Stiffened Panels for Marine Applications

The use of high-strength aluminum alloys in marine construction has certainly obtained many benefits, particularly for building fast ferries and also for military purposes. It is commonly accepted that the collapse characteristics of aluminum structures are similar to those of steel structures until and after the ultimate strength is reached, regardless of the differences between them in terms of material properties. However, it is also recognized that the ultimate strength design formulas available for steel panels cannot be directly applied to aluminum panels even though the corresponding material properties are properly accounted for. This is partly due to the fact that the stress versus strain relationship of aluminum alloys is different from that of structural steel. That is, the elastic-plastic regime of material after the proportional limit and the strain hardening plays a significant role in the collapse behavior of aluminum structures, in contrast to steel structures where the elastic perfectly plastic material model is well adopted. Also, the softening in the heat-affected zone significantly affects the ultimate strength behavior of aluminum structures, whereas it can normally be neglected in steel structures. In this paper, the ultimate strength characteristics of aluminum plates and stiffened panels under axial compressive loads are investigated through ANSYS elastic-plastic large deflection finite element analyses with varying geometric panel properties. An "average" level of welding-induced softening and initial imperfections is assumed for the analyses. Closed-form ultimate compressive strength formulas for aluminum plates and stiffened panels are derived by regression analysis of the computed results.

Indentation creep of heterogeneous blends of poly(ethylene terephthalate)/impact modifier

The indentation of a sphere into a flat support under a constant load provides information on the resistance of polymeric materials to pressure, which may be of basic importance in various applications. The existing theoretical background for indentation creep in an elastic–plastic regime is reviewed briefly. The indentation creep was measured over the interval 0.1–100 min; in addition, five auxiliary measurements lasting 0.4, 1, 4, 10 and 40 min were performed with the same load. After a recovery period 10 times longer than the creep time, the irreversible part of the indentation depth was read off. The acquired experimental data were fitted with a suitable function in order to calculate irreversible deformation for any time in the interval 0.1–100 min. An essential part (up to 50%) of the indentation depth was found to be irreversible; plastic deformation grew with the creep time somewhat faster than total deformation. Indentation mainly proceeded in short periods after the initiation of loading, while a further increase in penetration depth was much slower; however, no “break” was observed in the time dependencies of measured properties. The acting pressure was linearly decreasing with the logarithm of time due to the rising penetration depth and contact area in the course of individual measurements. The penetration depth/sphere radius ratio was in all cases smaller than 0.10. The logarithm of compliance, which was proportional to the fraction of impact modifiers, was for all samples a linear function of the logarithm of creep time. Although the slope of these dependencies was rather small, it increased with the modifier content, thus indicating the rising creep rate. The effects of two types of impact modifiers on the indentation creep of PET were virtually identical.

A Semi-Analytical Solution for the Sliding Inception of a Spherical Contact

A finite element analysis, for an elastic perfectly plastic sphere normally loaded by a rigid flat, is combined with an approximate analytical solution to evaluate the maximum tangential load (static friction) that can be supported by the spherical contact at the inception of sliding. Sliding inception is treated as a failure mechanism based on plastic yield rather than a Coulomb friction law with a certain friction coefficient. Two different failure modes are identified, either on the contact area or below it, depending on the elastic-plastic status of the normal preloading. A limiting normal preload is found above which the contact cannot support any additional tangential load. Simple analytical expressions for an “internal static friction coefficient” are presented for both the elastic and the elastic-plastic regimes.

The study of the filtration of liquids in the elastic-plastic regime with the integral law of fracture of rocks

As experience shows the development of deep oil fields with terrigenous reservoirs along with irreversibility of deformation there is a loss of stability of the formation's skeleton, i.e. he collapses in zones of strong pressure decrease. Particles of rock then are carried out from the formation by a flow of liquid. In this case, the composition of the liquid changes, a two-phase medium consisting of a liquid and a solid particles. In this paper we propose generalized dependencies of the variation porosity and permeability in the elastic-plastic mode of filtration The liquid taking into account the removal of the destroyed particles from the formation, where it is taken into account non-local character of the removal of the destroyed particles in time.

Plastic deformation of III–V semiconductorsunder concentrated load

The paper reviews the plastic behaviour of III–V semiconductors under concentratedload and its implication for optoelectronic-device design. We consider first, fundamental aspects involved into the mechanical resistance to contact loading of semiconductor single crystals (elastic-plastic transition, strain field, hardness-yield relationship). The paper then describes recent studies of applications aimed at improving the heterostructure quality used in optoelectronic applications and emphasizes the so-called mechanical design (alloying and compliant substructure). Semiconductor technology offers model materials with high crystalline quality whileits demand for improving heterostructure quality is a challenge to the Materials Science community. The elastic-plastic transition and subsequent plastic flow under contact loading is complex and has been widely investigated. This is reviewed integrating most recent works made using instrumental nano-indentation that allows monitoring the penetration of a diamond tip as a function of the applied load. Furthermore, this technique allows deformation in the micro- and milli-newton regime so that fracture can be avoided and the first steps of plastic deformation can be investigated. In particular, the determination of the plastic onset and hence the yield strength is possible by investigating the transition between elastic and elastic-plastic regime and measuring the plastic zone size as a function of the applied load. Results for various III–V semiconductors are reported. On the other hand, the performance of heterostructures is directly dependent on the density of dislocations that relax the lattice mismatch between the substrate and the layers. Nanoindentation allows for a better understanding of the plastic deformations in such structures and opens practical routes to improve the devices. For instance, to avoid the generation of threading dislocations, compliant substructures are now developed in order to concentrate the plastic relaxation underneath the heterostructure. Nano-indentation tests on such structures are reported and the results show that the yield strength of the substrate can be reduced using a compliant substructure. In fact, mechanical design of optoelectronic devices should be considered throughout the fabrication process.

Quasi-static response of laterally simple compressed hexagonal rings

This paper presents a study on the load-compression and energy absorption characteristics of a laterally simple crushed hexagonal ring. Two cases are considered: crushed across faces and comers. The initial part in the load-displacement trace shows a linear elastic characteristic followed by a non-linear elastic-plastic regime before collapse. The collapse load in ring compressed across faces is higher than that compressed across comer by factor of 1.8 for all cases. A simple but elegant analysis is also carried out. Experimental observations are compared with simple theoretical analyses as well as Finite Element formulation and good agreements are seen.

Plastic zone development in dynamic tear-type test specimens

The J-integral is a fracture criterion, which permits measurement of the fracture toughness of a specimen where fracture occurs in the elastic–plastic regime. An understanding of the ratio of plastic zone size (radius) to the crack tip blunting (stretch zone) is required to determine the upper temperature for transition curves, where elastic–plastic fracture becomes invalid and general yielding occurs. This study endeavors to acquire this ratio using finite element techniques. The development of the plastic zone in dynamic tear (DT) specimens and non-standard three-point bending fracture test specimens was the main focus of the study. The ABAQUS finite element software was used to model the elastic–plastic behaviour of the specimens. The cracks in the specimens were induced by pressing the notch followed by fatigue cracking at 30–40% of the limit loads. The shapes of these cracks were adequately modelled in the finite element analysis. The specimens were made of 350WT steel and 304 stainless steel materials and were loaded until fixed amounts of permanent deformation were recorded. Results were obtained in the form of plots, showing the progression of the plastic zone around the crack tip. For each case, mid-point plastic deflection, stretch zone width and plastic zone radius were computed.

Numerical and experimental determination of three-dimensional multiple crack growth in fatigue

This work is concerned with the assessment of propagation of multiple fatigue cracks in three-dimensions. Computational modelling of fatigue crack propagation is made together with detection and monitoring of the crack shape development. The boundary element method (BEM) is used for automating the modelling of crack propagation in linear elastic as well as elastic–plastic regimes. Strain at several positions on the specimen surface near the crack mouth is measured to monitor crack initiation, shape development and closure levels. Examples are provided to validate the model by comparing the experimental results with those obtained by numerical predictions.

A study of the restitution coefficient in elastic-plastic impact

The aim of this work is to provide useful quantitative support for theories of the restitution coefficient for normal impacts involving plastic deformation, especially in the region close to the threshold at which plastic deformation begins. The impacts were from spheres of 5 mm diameter of aluminium oxide (which deformed elastically), dropped on to thick plates of mild steel or aluminium alloy. Very accurate measurements of impact and rebound velocities were made for drop heights from 1.75 m down to 0.6 mm, covering a range of velocities down to the yield threshold. Most of these results are in the elastic-plastic velocity range over which the indentation pressure varies from its value at initial yield of about 1.1sigmay to the value when full plasticity is established of about 2.8sigmay. The variation in the restitution coefficient with velocity in this range closely fits the rebound model of Tabor, which allows the indentation pressure to vary through the Meyer index n. The fitted values of n take into account these elastic-plastic effects as well as work hardening, demonstrating that a power-law compliance relationship is a very good model for the increase in indentation pressure as plasticity develops. Full plasticity only becomes established at impact velocities which are of the order of 100 times the velocity at which initial yield takes place. Models which assume a constant indentation pressure (perfect plasticity) are not a good match for the data in the elastic-plastic regime.

Transferability of results of PTS experiments to the integrity assessment of reactor pressure vessels

The integrity assessment of the reactor pressure vessel (RPV) is based on the fracture mechanics concept as provided in the code. However, this concept covers only the linear-elastic fracture mechanics regime on the basis of the reference temperature RT NDT as derived from Charpy impact and drop-weight test. The conservatism of this concept was demonstrated for a variety of different materials covering optimized and lower bound material states with regard to unirradiated and irradiated conditions. For the elastic-plastic regime, methodologies have been developed to describe ductile crack initiation and stable crack growth. The transferability of both, the linear-elastic and elastic-plastic fracture mechanics concept was investigated with the help of large scale specimens focusing on complex loading situations as they result from postulated thermal shock events for the RPV. A series of pressurized thermal shock (PTS) experiments were performed in which the applicability of the fracture mechanics parameters derived from small scale specimen testing could be demonstrated. This includes brittle (static and dynamic) crack initiation and crack arrest in the low Charpy energy regime as well as stable crack initiation, stable crack growth and crack arrest in the upper shelf toughness regime. The paper provides the basic material data, the load paths, representative for large complex components as well as experimental and theoretical results of PTS experiments. From these data it can be concluded that the available fracture mechanics concepts can be used to describe the component behavior under transient loading conditions.

Elastic-plastic indentation creep of glassy poly(methyl methacrylate) and polystyrene: characterization using uniaxial compression and indentation tests

This paper discusses the time-dependent mechanical response of poly(methyl methacrylate) (PMMA) and polystyrene (PS) subjected to a shallow indentation made by a 750 µm radius steel ball at 25 °C. The penetration depth was measured as a time-response to a prescribed loading history of the indenter. The tests were performed in the intermediate elastic-plastic regime, which is of paramount importance when dealing with the mechanics of a multicontact interface between rough bodies. The creep characteristics under constant load were analysed with an Eyring law relating the average stress and the strain rate in the deformed volume. The results were compared to data obtained by a standard uniaxial compression test on the bulk material. We have deduced a simple empirical rule which accounts for the heterogeneous stress and strain fields under the indenter and reduces the intricate problem of elastic-plastic indentation creep to an effective scalar rule.