Elastic-plastic Fracture Mechanics Research Articles

3D J-integral evaluation for solids undergoing large elastic–plastic deformations with residual stresses and spatially varying mechanical properties of a material

In this paper, a 3D J-integral based on the domain integral approach is presented for large deformation elastic–plastic fracture mechanics problems associated with residual stresses and spatially varying mechanical properties of a material. The proposed 3D J-integral has physical significance as the energy dissipation into the process zone. The derivations of the proposed J-integral are presented in detail. Through numerical examples, it is shown that the proposed J-integral is unconditionally path independent. The present formulation is a rigorous extension of the 2D-Tε∗ integral of Okada and Atluri to 3D.

Investigation of crack propagation in the surface white layer of rail steel

Introduction . The paper is devoted to the evaluation of cracking of white layers formed on the surface of the rail while in operation. Cracks are detected in the white layer of rail steel after one thousand test cycles. This is due to tensile and shear stresses on the surface of the wheel-rail contact spot. The paper presents the study results of the morphological characteristics of the white layer on the rail surface. Materials and Methods . The object of study (rail surface after operation) was examined under a microscope. Then, a two-dimensional model of finite elements of the plane deformation was developed to simulate the dynamic characteristics of the white layer cracking. Mathematical models describing crack propagation are proposed. For this, we applied the criterion of the elastic plastic fracture mechanics, the J -integral method. The SYSWELD program performed numerical modeling of the formation of a white layer and the distribution of residual stresses. Results . Optical images of the microstructure of the cross section of a white layer on the rail surface after operation are presented. Two different types of cracks were fixed at the trailing edge of the white layer of the samples studied. The SYSWELD program visualized fragments of simulating the mechanism of the white layer formation with the distribution of residual stresses, compression, and tension. The calculation results show that the values of the J -integral for all three cracks slightly decrease if the crack length reaches 10-50 gm. Discussion and Conclusions . The results obtained are applicable to assess the wear resistance of rail steels and predict the direction of crack growth. Comparisons of J -integral maxima have shown that under identical load conditions, crack no. 1 is likely to grow faster than cracks nos. 2 and 3. With an increase in the length of the crack, the maxima of the J -integral of all three cracks decreased.

Fatigue crack growth prediction for small-scale yielding (SSY) and non-SSY conditions

A model to predict fatigue crack growth (FCG) for small-scale yielding (SSY) and non-SSY conditions where J-integral applies is established. The ΔJ-characterized elastic-plastic fracture mechanics (EPFM) analysis is performed based on a rearranged FCG process to achieve the crack-tip geometry and stress state. The root stress of blunted crack and the FCG rate are calculated from the cycle-wise local and global energy balance. To consider effects of geometry, load level and strain hardening, a correction factor is further developed in the governing equation of global energy balance. The model is validated using the test data of several types of metals.

Fracture toughness testing at the micro-scale − The effect of the unloading compliance method

Fracture mechanical testing of micro-sized cantilevers was conducted in order to quantify the fracture toughness and behaviour of the (1 0 0)[0 1¯ 1] crack system in α-iron at 37.5 K, 133 K and room temperature. The cantilevers are outside the range of validity for linear-elastic fracture mechanics due to the small sample size, rendering the cantilevers out of bounds in relation to linear-elastic fracture mechanics and classical fracture mechanics. Elastic-plastic fracture mechanics has therefore been applied to determine the conditional fracture parameters KQC and JQC. A comparison between cantilevers continuously loaded with corrected dynamic stiffness measurements and another data set of cantilevers tested with the unloading compliance method has been made. A distinct difference in determined fracture toughness and crack behaviour was identified, indicating potential concerns when applying the unloading compliance method at the micro-scale on ductile materials.

Fracture Toughness of Hollow Glass Microsphere-Filled Iron Matrix Syntactic Foams.

In this study, iron-based metal matrix syntactic foam (MMSF) containing hollow glass microspheres as filler was investigated with respect to notch sensitivity aspects. The MMSF was produced by means of metal powder injection molding. The notch sensitivity was studied via (i) elastic-plastic fracture mechanics measurements (determination of R-curves based on three-point bending tests) and (ii) Charpy impact tests. In both cases, the samples were machined with two different (U- and V-shaped) notch geometries. The critical J-integral value was determined for both notch types, which resulted in lower fracture toughness values in the case of the V-shaped notches and thus notch sensitivity of the material. This finding can be connected to the characteristics of the deformation zone and the associated stress concentration at the tip of the machined notches. The results were confirmed by Charpy impact tests showing ~30% higher impact energy in the case of the U-shaped notch. The failure modes were investigated by means of scanning electron microscopy. In contrast to the bulk material, the MMSF showed brittle fracture behavior.

Microstructural characterization of the synergic effects of dynamic strain ageing and hydrogen on fracture behaviour of low-alloy RPV steels in high-temperature water environments

Tensile tests in high-temperature air with pre-charged hydrogen and elastic plastic fracture mechanics tests in hydrogenated high-temperature water (HTW) at 250 and 288 °C on low-alloy reactor pressure vessel (RPV) steels revealed a clear but moderate reduction of ductility and fracture resistance, respectively. The observed behaviour is a consequence of synergistic effects between hydrogen embrittlement (HE) and the dynamic strain ageing (DSA), in which the HE was amplified by a high DSA susceptibility. The deformation microstructures in the vicinity of the crack tips in air and HTW of two RPV steels with high DSA susceptibility were characterized in detail. These investigations support the idea that the environmental degradation of fracture resistance in hydrogenated HTW was mainly due to the plasticity localization by the interaction between DSA and hydrogen in RPV steels. Synergistic effects of DSA and hydrogen lead to heterogeneous distribution of dislocations and formation of dislocation cells inside bainitic laths.

Fracture toughness anisotropy of ultrafine-grained pure copper processed by equal channel angular pressing

The fracture anisotropy of ultrafine grained pure Cu processed by eight passes of equal channel angular pressing in route BC was investigated based on elastic-plastic fracture mechanics. For different crack planes and different crack propagation directions, both the global fracture initiation toughness measured by JIC and KIC and the crack growth toughness represented by the non-dimensional tearing modulus TR were evaluated by accurately determining the J-integral resistance curves. Furthermore, the crack tip opening displacements at fracture initiation were also measured through crack profile analysis to determine the local crack initiation J-integral Ji. The results demonstrate that the specimen orientation has a pronounced influence on the fracture toughness of the ultrafine grained Cu. Among all the tested orientations, the fracture resistance is highest in the transverse direction with KIC = 99 MPa m1/2 and TR = 100, and lowest in the extrusion direction with KIC = 66 MPa m1/2 and TR = 30. The origin causing the anisotropic fracture toughness is discussed based on detailed fracture appearance characterization and microscale crack path analysis.

The Characteristics of Selected Triaxiality Measures of the Stresses for a C(T) Specimen Dominated by the Plane Strain State

The paper presents a comprehensive analysis of the stress field and selected triaxiality parameters near the crack tip for C(T) specimen dominated by the plane strain state using the finite element method. It includes some theoretical information about elastic-plastic fracture mechanics, the basics of the FEM modeling and presentation of the numerical results. The FEM analysis includes calculations with large strain assumptions. The influence of the external load and crack length is discussed. Additional elements of the paper are a qualitative assessment of the size of plastic zones and the crack tip opening displacement.

The effect of crack-tip constraint in some problems of fracture mechanics

The effect of in-plane and out-of-plane crack-tip constraint parameters, namely, the non-singular T-stress components and the parameter A, in some problems of elastic and elastic-plastic fracture mechanics is discussed. The three-dimensional crack tip stresses including the non-singular T-stress components are employed to describe the crack tip plastic zone, the failure assessment diagrams and the constraint-dependent fracture toughness for a solid with a finite notch/crack under mode I loading and different angles of surface crack growth under conditions of rolling-sliding. Theoretical and numerical aspects of the two-parameter J-A approach in elastic-plastic fracture mechanics are presented in connection with crack-tip constraint. It is shown that the parameter A can be introduced in a fracture criterion as a constraint parameter.

Experimental and computational investigation on dynamic fracture toughness (J1d) behavior of multi-pass SMA armor steel weldments

Dynamic fracture toughness (J1d) behavior of shield metal arc (SMA) welding of armor grade Armox 500 T steels prepared with low hydrogen ferritic steel (LHF) and austenitic stainless (ASS) steel consumables have been evaluated and compared. Three different techniques have been described and implemented to evaluate the dynamic fracture toughness (J1d) of investigated materials. Further, the results have been compared with Elastic plastic fracture mechanics (EPFM) approach. An investigation has also been performed regarding the influence of microstructures (for LHF and ASS weldments fusion zone) effect on dynamic fracture toughness (J1d) and fracture characteristic. Finally, a constrained optimization procedure of minimizing the mean absolute percent error (MAPE) has been used to determining the Johnson Cook (JC) hardening and Damage model for Armox 500 T to simulate the impact and damage behavior. Results revealed that, Dynamic fracture toughness (J1d) of weldment-2 (prepared by ASS consumables and consisted duplex microstructure) is 20% and 10% more than weldments-1 (prepared by LHF consumables and consisted acicular ferrite structure) and counterpart base metal (Armox 500 T). The MAPE and standard deviation between FEA and experimental results are less than 10% with a good value of regression coefficient (R) which shown the excellent prediction capability of developed model.

Fracture Behaviour of Collagen: Effect of Environment

Collagen forms one-third of the human-body proteome and finds a wide range of applications in a biomedical field thanks to its mechanical stability, biocompatibility and biodegradability. Collagen can be produced in a form of films suitable for scaffolds, tissue regeneration, flexible electronics etc. significant differences in the mechanical properties were observed for collagen films tested in-aqua environment. Considering this and potential biomedical applications of collagen films, their mechanical testing should be performed in aqua to mimic the in-vivo conditions. Hence, this study reported the fracture behaviour of collagen in-aqua compared with that at ambient (in-air) loading conditions. Single-edged notched tension (SENT) specimens of collagen films demonstrated completely different stress-strain curves in-aqua conditions. A reduction in their tensile strength (by 90%) and fracture energy (by 40%) accompanied with an increase in the failure strain (by 1600%) was observed for such conditions. Crack propagation was rapid for in-air specimens, with a brittle failure, while for in-aqua specimens the crack opening was rather slow and accompanied with by crack blunting, leading to large plastic deformation (ductile failure). These behaviours encouraged the quantification of the fracture toughness of collagen films using different fracture toughness parameters: KIC (linear elastic fracture mechanics) for in-air specimens and JC-integral (elastic-plastic fracture mechanics) for in-aqua specimens.

Time-dependent fracture of epoxy resin under mixed-mode I/III loading

In this study, fracture behavior of epoxy resin under mixed-mode loading between opening mode (mode I) and out-of-plane shearing mode (mode III) was investigated using an adjustable loading fixture set with a single-edge notched tension (SENT) specimen. Effects of specimen thickness and loading rate were investigated. Two different thicknesses of specimen were employed (4 and 8 mm) And, the fracture toughness tests were performed at two different loading rates of 0.1 and 1000 mm/min. Fracture toughnesses of epoxy resin were calculated using finite element (FE) analysis based on both linear-elastic fracture mechanics (LEFM) and elastic–plastic fracture mechanics (EPFM). It was found that under mixed-mode I/III and pure mode III loadings, fracture occurred in a ductile manner with severe plastic deformation. Therefore, LEFM is no longer valid, and EPFM approach was applied in this study to characterised fracture behavior of epoxy resin under mixed-mode I/III loading. Two different fracture mechanics parameters based on EPFM, e.g. critical J-integral (Jc) and critical crack-tip displacement, were calculated. Jc results revealed that the effect of specimen thickness was significant at low loading rate. However, at high loading rate the effect of specimen thickness was marginal. While, critical crack-tip displacement results indicated that fracture occurred at the same level of crack-tip displacements regardless of specimen thickness. An observation of fracture surfaces agreed with the crack-tip displacement results, i.e., a similar fracture surface topology for both thick and thin specimens tested at the same loading rate.

Rising R-curves in particulate/fiber-reinforced resin composite layered systems

BackgroundAn anisotropic fracture behavior has already been successfully induced in a condensable resin composite by reinforcement with discontinuous glass fibers, developing a steep rise in the fracture resistance curve. There is still the need for developing such concepts further, by evaluating the behavior of layered structures that attempt to replicate the natural gradient structure of enamel and dentin. MethodsMonolithic and bilayer specimens of a flowable short-fiber particulate-reinforced composite (SFPRC) material (GC Corp.) and a commercial flowable particulate-reinforced composite (PRC) (Essentia HiFlo, GC Corp.) were produced with the fibers aligned perpendicular or randomly oriented to the plane of crack propagation. Pre-cracked specimens were tested in 3-point bending using the single-edge-V-notch-beam method with accurate displacement tracking recordrecord. Controlled crack growth experiments were conducted at progressive crack extension intervals to build R-curves using linear-elastic and elastic-plastic fracture mechanics. ResultsWe demonstrate firsthand the development of R-curves in resin composite bilayers, with crack arrest at the interface and a steep rise in crack resistance with subsequent drop within the SFPRC layer. Crack deflection and fiber bridging were found to contribute to a higher rise in the R-curves for specimens with aligned fibers; still, randomly oriented fibers showed significant R-curve development, especially at short range intervals. An increase in the vol% of fibers and a decrease in the Young's modulus contributed to a higher overall performance of the flowable vs. the condensable SFPRF materials. ConclusionsSFPRC materials show an up to 5-fold improvement in the fracture resistance over conventional PRCs, and show the potential to be used to build gradient structures by varying the fiber alignment and fibers parameters (length and packing).

Short fatigue crack behaviour of LZ50 railway axle steel under multi-axial loading in low-cycle fatigue

An experimental study was carried out on the low-cycle fatigue of LZ50 railway axle steel under multi-axial loading. The initiation and propagation behaviour of a short fatigue crack was observed and analysed as per the principles of effective short fatigue crack. Our results showed that in the microstructurally short crack (MSC) stage, the crack propagation was strongly influenced by the microstructural features of the material and did not satisfy the linear elastic fracture mechanics. At the physically short crack (PSC) stage, the crack was long enough to not be directly influenced by the microstructures; nevertheless, linear elastic fracture mechanics still could not explain the law of crack propagation properly owing to the large-scale yield range of the crack tip. Based on these observations, a crack growth rate model under multi-axial loading was presented to explain the short fatigue crack behaviour. The non-linear elastic-plastic fracture mechanics parameter, J-integral (cyclic), was adopted as the driving parameter in this model and the crack closure effect was also taken into account. In the MSC stage, the crack growth rate fluctuated significantly when the cyclic J-integral was used owing to the influence of the microstructure. However, at the PSC stage, the crack growth rate fluctuations were small. A linear correlation for the PSC was obtained with R = 0.934 and this model could be applied to describe the short fatigue crack behaviour in the PSC stage.

Biaxial fatigue crack propagation behavior of ultrahigh molecular weight polyethylene reinforced by carbon nanofibers and hydroxyapatite.

Ultrahigh molecular weight polyethylene (UHMWPE) artificial joint has remained the preferred polymer component in total joint replacement surgery. However, more and more concerns have been raised about the failure of UHMWPE components due to the initiation and propagation of cracks at the notches with fixed functions. For this reason, biaxial fatigue crack growth (FCG) experiments of UHMWPE reinforced by carbon nanofibers (CNF) and hydroxyapatite (HA) were carried out using elastic-plastic fracture mechanics theory. The FCG resistance of UHMWPE, UHMWPE/CNF, and UHMWPE/HA was compared, and the effects of stress ratio (R) value and phase difference on FCG rate were investigated. At the same time, the influence of loading path was considered, and the corresponding crack path was analyzed. Results suggest that UHMWPE/CNF has better FCG resistance and the FCG rate increases with the increase of R value and the existence of 180° phase difference. In addition, crack bifurcation behavior is not observed under nonproportional loading conditions. The findings in this study will provide experimental validation and data support for better clinical application of UHMWPE-modified materials.

The effect of out-of-plane constraint on the stress fields near the front of a crack in a thin ductile plate

Classical plane solutions based on the elastic-plastic fracture mechanics are applied widely in practical engineering. These plane solutions follow the plane stress or plane strain assumption. However, in the case of a thin ductile plate with a through-thickness crack under tension, plane stress conditions exist at a distance of about one half of the plate thickness ahead of the crack front cross the thickness of the plate. What is the stress state in the region where both plane strain and plane stress conditions cannot be met? In the current paper, a semi-analytical method is presented to investigate the problem. Three dimensional Maxwell stress functions, the minimum complementary potential energy principle and three dimensional J-integrals are employed to obtain solutions for crack front fields in a thin ductile plate. Three-dimensional finite element (FE) analyses are carried out to verify the current solutions. FE results reveal that the out-of-plane constraint level Tz increases with increasing remote loading near the crack front. FE results also show that the in-plane stress fields near the crack front can be characterized by the current J-Tz solutions. Both FE and theoretical results illustrate that opening stresses decrease gradually to the corresponding plane stress HRR-field solutions with increasing radial distance r from the crack front in the mid-plane when remote loading is large enough.

Higher order J-Tz-AT solution for three-dimensional crack border fields in power-law hardening solids

Higher order J-A2 solution has been developed to improve the HRR singular solution under ideal plane strain conditions in power-law hardening solids with the the second A2 being considered to take into account of the in-plane constraint effect, and the J-Tz singular solution has been obtained for three-dimensional (3D) cracked body by introducing the out-of-plane stress constraint factor Tz. Here a higher order J-Tz-AT solution is developed on the basis of the J-Tz and J-A2 solutions and validated against comprehensive 3D finite element (FE) analyses for specimens with through-thickness, surface, embedded and corner cracks. It is shown that better agreements are obtained between the higher order J-Tz-AT solution and 3D FE results in all simulated conditions than previously available two- or three-parameter solutions. For specimens of high in-plane constraint, such as the single-edge cracked tension specimen, compact specimen and single-edge-notched bending specimen under three-point bending, the J-Tz leading singular solution itself shows sufficient accuracy. This universal characterization of crack border stress fields confirms that the developed J-Tz-AT solution combines the advantages of the J-Tz and J-A2 solutions, which can service as a solid foundation of elastic-plastic fracture mechanics.

Pure mode II fracture analysis of dissimilar Al-Al and Al-Cu friction stir welded joints using the generalized MTS criterion

Aluminum and copper, two highly desired material, are the most consumed minerals in different industries after iron and two most important materials in today’s industrial world. Copper for its beneficial properties like thermal and electrical conductivity and resistance to corrosion and aluminum for its low weight along with high strength are used extensively especially in the aerospace industry. Newly advanced friction stir welding (FSW) made these two materials with low weldability to be connected well together. In this study, mode II fracture of dissimilar friction stir welded joints made of AA7075-T6 and AA6061-T6, which are very popular in the aerospace industry, and also AA7075-T6 to copper are investigated by means of the cracked semi-circular bending (CSCB) specimen. According to ductility nature of the welded joints and formation of the substantial plastic zone around the crack tip at the crack growth instance, a study of failure requires elastic-plastic fracture mechanics. Since these criteria are intricate and laborious, a new approach is therefore needed to overcome this problem. A different approach to the traditional problem is given in the Equivalent Material Concept (EMC). By merging the EMC with the Generalized maximum tangential stress (GMTS) criterion (a brittle fracture criterion), the ultimate load of the friction stir welded of CSCB specimens is estimated. Theoretical results go beyond experimental reports, showing that the proposed criteria could meticulously predict the load carrying capacity (LLC) of the CSCB specimens.

In situ study on fracture behaviour of white etching layers formed on rails

Failure in engineering materials like steels is strongly affected by in-service deleterious alterations in their microstructure. White Etching Layers (WELs) are an example of such in-service alterations in the pearlitic microstructure at the rail surface. Cracks initiate in the rails due to delamination and fracture of these layers and propagate into the base material posing severe safety concerns. In this study, we investigate the microscale fracture behaviour of these WELs. We use in situ elastic-plastic fracture mechanics using J-integral to quantify the fracture toughness. Although usually assumed brittle, the fracture toughness of 21–25 MPa√m reveals a semi-brittle nature of WELs. Based on a comparison of the fracture toughness and critical defect size of WELs with the undeformed pearlitic steels, WELs are detrimental for rails. In the micro fracture tests, WELs show crack tip blunting, branching, and significant plasticity during crack growth due to their complex microstructure. The fracture behaviour of the WELs is governed by their microstructural constituents such as phases (martensite/austenite), grain size, dislocation density and carbon segregation to dislocations and grain boundaries. We observed dislocation annihilation in some martensitic grains in the WELs which also contributes to their fracture behaviour. Additionally, the strain-induced transformation from austenite to martensite affects the crack growth and fracture.

Fracture Mechanism and Fracture Toughness at the Interface Between Cortical and Cancellous Bone.

The microstructure at the interface of cortical and cancellous bone is quite complicated. The fracture mechanisms at this location are necessary for understanding the comprehensive fracture of the whole bone. The goal of this study is to identify fracture toughness in terms of J integral and fracture mechanism at the interface between cortical and cancellous bone. For this purpose, single edge notch bend (SENB) specimens were prepared from bovine proximal femur according to ASTM-E399 standard. Bone samples were prepared such that half of the sample width consists of cortical bone and other half of the width was cancellous bone; this interfacial bone is referred as a corticellous bone. Elastic-plastic fracture mechanics was used to measure fracture toughness. The J integral (both elastic and plastic) was used to quantify the fracture toughness. The plastic part of J integral value (Jpl) of corticellous specimen was 9310 J m-2, and shown to be 27 times of the J integral of the elastic part (Jel), 341 J m-2. The total J integral of the corticellous bone was found to be 9651 J m-2, which is close to two times of the cortical bone, 4731 J m-2. This study observed that J integral of corticellous bone is higher than the cortical bone since more energy is required for plastic deformation of corticellous bone due to crack branches and slowdown at the interface between cortical and cancellous bone.