Crack Tip Stress Research Articles

Roles of microstructures in high-cycle fatigue behaviors of 42CrMo high-strength steel under near-yield mean stress

In this study, high-cycle S-N characteristics and fatigue cracking behaviors under near-yield mean stress of 42CrMo steel with two different fine/coarse-grain tempered sorbite/bainite microstructures (FGM/CGM) were investigated. The results show that fatigue strength is greater for FGM than for CGM as expected, but fatigue crack growth (FCG) threshold is higher for the latter. Compared to FGM with a single crack source, CGM has multiple fatigue sources together with higher-degree ratchetting-fatigue damage, i.e., plastic-strain, dislocation cells and sub-grains, thus accelerating fatigue crack initiation. In the near-threshold regime, roughness-induced crack closure in coarse-microstructures of CGM leads to FCG retardation behavior, which increases FCG threshold. In the Paris regime, CGM presents a similar FCG rate to FGM. Microstructure barriers (i.e., crystal interfaces, carbides and interfaces with different orientations), secondary cracks, crack-path fluctuations, ratchetting and plastic strain jointly result in severer crack-tip stress shielding effects in CGM than in FGM. However, fatigue crack tends to propagate through the high Schmid factor region with {110}<111> slip system with lower slip resistance in FGM but not in CGM, which facilitates fatigue cracking of the former. Under the combined effects of the above factors, similar FCG rates are thus exhibited in both steels with different tensile strengths.

Tensile strength and crack tip stress distribution of modified glass in the composite laser beam separation

The tensile strength of the modified cross-section (MCS) determines to a certain extent whether the composite laser can complete the separation of glass, and the quality and efficiency of the separation. In this work, the effect of the picosecond Bessel laser on the tensile strength of soda-lime glass was systematically investigated for the first time. The relationship between the tensile strength and residual stress was not negatively correlated absolutely. The tensile strength was also related to the homogeneity and micro-structure of MCS, including micro cavities, cracks, and voids. Meanwhile, it was pointed out that by selecting appropriate modified parameters, the plasma shielding effect can be suppressed and the micro-morphology of MCS can be controlled to obtain smaller tensile strength and better cutting quality. Secondly, the stress field distribution at the crack tip was simulated to analyze the mechanism when the continuous wave (CW) laser interacted with the modified glass. The simulation results showed that only the stress perpendicular to the laser incidence direction and the scanning direction exceeded the tensile strength of glass material, ensuring that the cracks propagated only along the MCS. Finally, one-time separation of glass was achieved by using a composite laser beam separation (CLBS) technology with a speed of 50 mm/s, which was comparable to the industrial level, and the roughness of separated sidewall was less than 0.5 μm.

Modeling Corrosion Product Film Formation and Hydrogen Diffusion at the Crack Tip of Austenitic Stainless Steel.

Corrosion product films (CPFs) have significant effects on hydrogen permeation and the corrosion process at the crack tip. This paper established a two-dimensional calculation model to simulate the formation of CPFs at the crack tip and its effects on the crack tip stress status and hydrogen diffusion. The CPFs were simplified as a single-layer structure composed of Fe2O3, the effective CPFs boundary was modeled by the diffusion of oxygen, and the CPF-induced stress was modeled by hygroscopic expansion. The simulation was conducted with two stages; the first stage was to simulate the formation of CPFs formation and its effects on the crack tip stress status, while the second stage focused on the hydrogen diffusion with and without CPF formation under different external tensile loads. The results indicate that the highest compressive stress induced by the formation of CPFs is located at 50~60° of the crack contour and dramatically weakens the crack tip tensile stress at low-stress status. The CPFs can inhibit the hydrogen permeation into the crack tip, and the hydrostatic pressure effects on the redistribution of the permeated hydrogen are significant under larger external load conditions.

Characterization of crack-tip fields for elastoplastic fatigue crack growth Part II: Effects of crack closure and in-plane constraint

The crack-tip fields of elastoplastic fatigue crack growth with crack closure are studied and correlated to the ΔJ-integral. Computational results confirmed that the singularity of the effective stress ranges of the opening process reduces with increasing crack closure, whereas the effective stress ranges from the closing process possess the known HRR solution form. The far-field ΔJeff-integral can be used to characterize the crack-tip field stress in the closing process, which is not affected by the loading ratio and by the path dependence of the ΔJ-integral. Based on extensive FEM computations, an estimation formula for the effective ΔJeff-integral was proposed for various loading ratios and plastic hardening materials. The in-plane constraint effects in fatigue crack growth can be quantified based on the J−Q concept of elastoplastic fracture mechanics, within the frame of ΔJeff-Q characterization. The relationship between Q and the transverse stress defined in the closing processes was established for a quantitative description of the crack tip constraint.

Multimaterial Topology Optimization of Adhesive Backing Layers via J-Integral and Strain Energy Minimizations

Abstract Strong adhesives often rely on reduced stress concentrations obtained via specific functional grading of material properties. This can be seen in many examples in nature and engineering. Basic design principles have been formulated based on parametric optimization, but a general design tool is still missing. We propose here the use of topology optimization to achieve optimal stiffness distribution in a multimaterial adhesive backing layer, reducing stress concentration at selected (crack tip) locations. The method involves the minimization of a linear combination of (i) the J-integral around the crack tip and (ii) the strain energy of the structure. This combination is due to the compromise between numerical stability and accuracy of the method, where (i) alone is numerically unstable and (ii) alone cannot eliminate the crack tip stress singularity. We analyze three cases in plane strain conditions, namely, (1) double-edged crack and (2) center crack, in tension, as well as (3) edge crack under shear. Each case evidences a different optimal topology with (1) and (2) providing similar results. The optimal topology allocates stiffness in regions that are far away from the crack tip, and the allocation of softer materials over stiffer ones produces a sophisticated structural hierarchy. To test our solutions, we plot the contact stress distribution across the interface. In all observed cases, we eliminate the stress singularity at the crack tip, albeit generating (mild) stress concentrations in other locations. The optimal topologies are tested to be independent of the crack size. Our method ultimately provides the robust design of flaw tolerant adhesives where the crack location is known.

Semi-analytical solution for internal forces of tunnel lining with multiple longitudinal cracks

Longitudinal cracks on the tunnel lining significantly influence the performance of tunnels in operation. In this study, we propose a semi-analytical method that provides a simple and effective way to calculate the internal forces of tunnel linings with multiple cracks. The semi-analytical solution is obtained using structural analysis considering the flexural rigidity for the cracked longitudinal section of the tunnel lining. Then the proposed solution is verified numerically. Using the proposed method, the influences of the crack depth and the number of cracks on the bending moment and modified crack tip stress are investigated. With the increase in crack depth, the bending moment of lining scetion adjacent to the crack decreases, while the bending moment of lining scetion far away from the crack increases slightly. The more the number of cracks in a tunnel lining, the easier the new cracks initiated.

Identifying crack tip position and stress intensity factors from displacement data

Identifying crack tip position and stress intensity factors from displacement data

Criteria for determining the fatigue limit of Ni-based superalloy 718, considering the competition between opening- and shear-mode fatigue crack-growth

The mechanism that determines the fatigue limit associated with small-crack arrest in Ni-based superalloy 718 remains under debate. In order to comprehensively assess the alloy’s fatigue limit in relation to the growth threshold of a small fatigue crack, (i) a ΔKI-decreasing fatigue crack-growth test, (ii) torsional fatigue tests and (iii) tension-compression fatigue tests were conducted under fully-reversed loading conditions. In addition, elastic, crack-tip stress fields were analyzed for cracks under various loading conditions. Based on the results, a novel strategy for evaluating the alloy’s fatigue limit is proposed after consideration of two crack-arresting modes (i.e., opening and shear modes).

Theoretical solutions for 2D mode-I crack-tip stress fields in power-law plastic materials based on the stress factor derived from the developed median-energy–density equivalence method

This study presents the energy density equivalence equation, demonstrating that the strain energy density of an arbitrary representative volume element (RVE) under a complex stress state equals to that under a uniaxial stress state when volume change is neglected. Based on the developed median-energy–density equivalence method, the analytical solution for equivalent stress of the RVE at the energy density equivalence point in power-law plastic materials is derived in a new method and the concept of stress factor is proposed. Additionally, novel special functions are introduced to accurately describe the angular distributions of stresses in this study. By combining the stress factor, integral theoretical solutions for mode-I crack tip stress fields in power-law plastic materials under finite plane conditions are proposed. Finally, parameterized studies are conducted on bending and tension specimens under plane-strain and plane-stress conditions. The results of stress distributions and contour lines predicted by the integral theoretical solutions are compared with the finite element analysis and HRR solutions for five mode-I plane specimens, providing verification of the solutions’ applicability.

Grain-level residual stress distribution at dwell fatigue crack tips in a nickel-based superalloy

Dwell fatigue crack growth in nickel-based superalloys is influenced by a complex interplay between mechanical and chemical phenomena. The stress distribution at the crack tip is closely related to these phenomena and to the local microstructure. In this study we evaluate experimentally the microscale residual stress distribution ahead of crack tips in RR1000 alloy samples after interrupted high temperature dwell fatigue testing. In the crack opening direction the results show a compressive residual stress zone, the extent of which is linked to the plastic zone size and crack growth retardation behaviour. In the direction of crack propagation the residual stress is also influenced by crystallographic grain orientation. The results demonstrate a novel approach of experimentally evaluating crack tip stress distribution via focused ion beam – digital image correlation (FIB-DIC) ring-core measurements at the grain-level. This provides new insights into fatigue crack growth in microstructurally heterogeneous materials.

The coupling effects of strain gradient and damage on Mode I crack tip stress fields

The cleavage fracture of metallic materials is determined by the crack tip stress field depending on plastic strain gradient and microstructural damage. The synergistic effects of strain gradient and damage on the stress fields near a Mode I crack tip in metallic materials are investigated using a modified conventional theory of mechanism-based strain gradient plasticity (CMSG). Besides preserving the essence of classical CMSG, a stress-dependent damage variable is introduced to characterize the effect of microstructural damage on the material's intrinsic length, elastic modulus and plastic yielding criterion. Based on the present theoretical model, it is found that the strain gradient and microstructural damage effects both are prominent in a small region near the Mode I crack tip, at which the damage evolution is determined by the strain gradient. Although the crack tip stress field with strain gradient and damage effects is lower than the existing ones influenced only by strain gradient, it is still significantly higher compared with the yielding strength of the material so that the cleavage fracture at the crack tip can be well explained. The damage-induced stress level reduction indicates that the stress concentration at the crack tip can be alleviated to inhibit the crack propagation. As a result, when the damage effect is considered, not only a larger external load is required to induce crack propagation but also the plastic region in front of the crack tip is enlarged, consequently leading to increases of fracture strength and energy dissipation in the material. The present research provides a more precise prediction of the crack tip stress distribution in metallic materials, which is helpful for better understanding the microscopic mechanism of the cleavage fracture phenomenon.

Failure analysis from microcracks to a dominant crack in MEMS thin films using combined damage and fracture mechanics

Reliability issues in MEMS devices are generally rooted in the evolution of microdefects in materials. Although the failure occurs at the top level of the device (macroscopic function), the root cause of the functional failure can be traced back to the bottom level (material micro defects). Therefore, it is crucial to consider the influence of material damage in the stress–strain constitutive equations to calculate the magnitude of crack propagation force. In this paper, a combined method of damage and fracture is considered for calculating the stress of crack tip of MEMS thin films. To calculate the initiations and growths of microcracks, continuum damage mechanics (CDM) is used. Based on the CDM method, a relationship between material degradation and the increase of electrical resistance is established. Through the established computational methods, we can perform a calculation analysis on the failure of MEMS caused by cracks. A multiscale quantification result establishes pairwise connections between material degradation characterization (damage D), crack propagation (tip stress K), and macroscopic performance (resistance R). This article provides a valuable theoretical basis for investigating the failure mechanisms of MEMS.

An efficient meshfree framework for simulation of crack tip stress fields in two-dimensional graded media subjected to thermoelastic loads

In the present work a novel framework of algorithm has been proposed for enhancing the versatility of the element-free Galerkin method for modeling of fracture in graded media subjected to thermoelastic loadings. The proposed work restructures the conventional element free Galerkin method (EFGM) at multiple level through generic MATLAB algorithms thereby developing an efficient and robust method for simulating crack tip stress fields in graded material subjected to thermoelastic loads. The proposed algorithm utilizes varying nodal density criterion in conjunction with optimum Gaussian quadrature around these nodes for numerical integration of the governing equations. The proposed algorithm also incorporates blended approximation which is effective for simulating crack tip stress fields in both convex and non-convex problem domains. Nonequilibrium formulation has been selected for evaluating stress intensity factors (SIFs) for the fracture problems in graded media. A few problems of cracked domain subjected to thermoelastic loads have been modeled and simulated to illustrate the effectiveness of proposed framework of algorithms. Further, three component level problems having non-convex domains have also been discussed to establish the robustness and modeling capabilities of the proposed work. A good agreement between the simulated results and reference data demonstrates the algorithm’s competence and robustness for modeling thermoelastic fracture in graded materials. The proposed methodology improves the computational efficiency and flexibility of the element-free Galerkin method for modeling thermoelastic fracture in graded media. Moreover, enhancement of computing speed with the proposed methodology adds to its modeling potential.

Geometry independent J-Tz domination of three-dimensional steady growing crack-tip fields in ductile materials

The crack-tip in-plane (Q and A2) and out-of-plane constraint (Tz) parameters have been extensively studied for ductile fracture problems on the basis of the pioneering HRR and J-Tz solutions. However, these analytic solutions rarely focus on the steady growing cracks, which play a vital role in J-R curve and integrity assessments of complicated structures. In this work, three-dimensional finite element method and GTN damage model are adopted to simulate quasi-static ductile crack growth under different plastic exponents, geometries and load levels. With the follow-up coordinate system, the J-Tz solution is extended to describe the crack-tip stress distributions of the quasi-static elastic–plastic growing cracks. It is found that in front of steady growth cracks, Tz strongly depends on specimen geometry. In the range of small-scale yielding, tensile stress and Tz gradually increase with increasing load J/JC. When the large-scale yielding stage is approaching, tensile stress and Tz tend towards a stable state. The maximum relative errors between the J-Tz solution and three-dimensional finite element results are 4.16% and 9.28% with J/JC smaller than 1 and 2, respectively. Such dominance and geometry independence of the leading order J-Tz solution make it more simply and effectively to assess the ductile fracture problems.

Effect of pre-crack non-uniformity for mini-CT geometry in ductile tearing regime

The mini-CT specimen attracts the attention from all over the world for application in fracture toughness measurement. However, one of the shortcomings of this geometry is related to the required tight accuracy of the specimen dimensions, in particular the fatigue pre-crack curvature which often violates the requirements of the ASTM standards. Given the limited thickness of mini-CT geometry, non-uniform pre-crack tends to develop during fatigue pre-cracking, resulting in a large proportion of mini-CT specimens being considered invalid.Previous investigations have demonstrated that mini-CT specimens with excessive crack front curvature can still provide meaningful fracture toughness results. In this paper, the effect of pre-crack front non-uniformity on ductile fracture is studied: first, the difference of macro parameters such as the applied load, J-integral and crack tip stress–strain field are investigated to illustrate the varying fracture behavior related to non-uniform pre-crack. Next, two micro-mechanics-based approaches, the Rice-Tracey void growth model and Thomason void coalescence model, are integrated to compare the ductile fracture initiation conditions associated with uniform and non-uniform fatigue pre-crack. Finally, the experimental verification of the ductile fracture simulations is performed for mini-CT specimens with uniform and 30° tilted initial cracks. The results indicate that the pre-crack non-uniformity plays a major role in the redistribution of local J-integral and stress–strain state, further affects the position of crack initiation and the early stages of crack propagation. Nevertheless, the pre-crack non-uniformity has limited effect on the global properties that are usually expected from fracture toughness tests, such as applied load, J-R curve and critical fracture toughness. The requirements in the ASTM E1820 regarding pre-crack front curvature need thus to be relaxed.

The applicability and the low limit of the classical fracture theory at nanoscale: The fracture of graphene

Miniaturization of mechanical structures offers excellent performances of the device while has brought problems of fracture at nanoscale. However, whether the classical fracture theory is applicable at such a small scale and what is its low limit are still challenging problems. In this paper, by conducting atomistic simulation of graphene and compared with the reported in-situ experiments, the applicable range of distance from crack tip for crack-tip stress distribution models and the low limit of crack length for fracture criterion are investigated. It is found that all crack-tip stress models are invalid within fracture process zone whose dimension is 2.5 Å away from crack tip. The energy-based fracture criteria are not applicable when the crack length is less than 8 nm due to the nonlinear stress–strain relationship, while the modified Griffith criterion can be applied to low limit of crack length 5 Å. For the stress-based fracture criterion, the stress intensity factor criterion fails when the crack length is less than 8 nm due to the decreasing size of critical K-dominant zone ΛK, while the theory of critical distances and quantized fracture mechanics can accurately predict the critical fracture stress regardless of the crack length, which can be unified by a non-local stress criterion. This work will provide a mechanical basis for the reliable application of the microelectronic devices at nanoscale.

Modified Model of Crack Tip Stress Field Considering Dislocation Slip Accumulation and Crack Tip Blunting

This study uses the digital image correlation technique to measure the crack tip displacement field at various crack lengths in U71MnG rail steel, and the interpolated continuous displacement field was obtained by fitting with a back propagation (BP) neural network. The slip and stacking of dislocations affect crack initiation and growth, leading to changes in the crack tip field and the fatigue characteristics of crack growth. The Christopher-James-Patterson (CJP) model describes the elastic stress field around a growing fatigue crack that experiences plasticity-induced shielding. In the present work, this model is modified by including the effect of the dislocation field on the plastic zone of the crack tip and hence on the elastic field by introducing a plastic flow factor ρ, which represents the amount of blunting of the crack tip. The Levenberg-Marquardt (L-M) nonlinear least squares method was used to solve for the stress intensity factors. To verify the accuracy of this modified CJP model, the theoretical and experimental plastic zone errors before and after modification were compared, and the variation trends of the stress intensity factors and the plastic flow factor ρ were analysed. The results show that the CJP model, with the introduction of ρ, exhibits a good blunting trend. In the low plasticity state, the modified model can accurately describe the experimental plastic zone, and the modified stress intensity factors are more accurate, which proves the effectiveness of dislocation correction. This plastic flow correction provides a more accurate crack tip field model and improves the CJP crack growth relationship.

A new and convenient method for strength evaluation of cracked cylindrical shell based on the ratio of crack tip stresses

A new and convenient method for the strength evaluation of cracked cylindrical shells under diverse loadings is presented according to stress intensity factor (SIF). In the proposed method, complicated SIF computation problem is simplified by extracting and eliminating the regularly parameters, and an analogy between reference problem and unknown problem is constructed. Then, based on the developed relations, the SIFs of unknown problems can be obtained conveniently by using the reference solution and FEM stress ratios. The proposed methodology removes the common computational difficulties for calculation SIFs and its accuracy is verified against published results. The practicality of present study is studied on several examples made up of common cylindrical shells in engineering. As the authors have found similar relationships in non-thin-walled structures, the present results might be more widely applicable and useful than those listed in this paper.

Preparation and mechanical properties of cubic boron nitride reinforced lead glaze layers of a gradient structure

Lead glaze possess excellent radiation ray shielding ability, and it is an efficient way to stop radiation spillover by using lead glazed indoor titles in a building. The merit of low firing temperature of lead glaze is, however, associated with its poor wear resistance. Here super-hard cubic boron nitride (cBN) particles, of a neutron shielding property, are introduced into the soft glass matrix to improve its mechanical properties. Results show that, at meticulously tailored conditions, the lead glaze surface is successfully enriched with cBN particles due to the lower density of cBN relative to the glaze. With 5 wt% cBN particles embedded in the glass matrix, the hardness increases by 51.2% and more importantly, the glaze yields significantly improved wear resistance. The finite element analysis reveals that the cBN particles enhance the toughness of the glaze, a key factor to wear resistance, by reducing the crack tip stress concentration.

Spatially resolved Raman piezospectroscopy for nondestructive evaluation of residual stress in β-Ga2O3 films

In this paper, the piezospectroscopic effect for β-Ga2O3, i.e. the spectral band shift in response to strain/stress, has been calibrated by the indentation method using spatially resolved Raman spectroscopy for quantitative stress evaluation of Ga2O3 devices, taking advantage of the crack-tip tensile stress field and the spatial probe deconvolution. A series of Vickers indentation prints were introduced on (010) and () Ga2O3 single crystals, and the relationships between observed band shifts and residual stresses were clarified to determine the phonon deformation potentials of the Raman bands. Accordingly, a quantitative analysis of the residual stress field in a Ga2O3 thin film grown on (0001) sapphire by plasma-assisted pulsed laser deposition, which revealed the presence of a gradient of incompletely released stress in the depth direction of the film, is shown as an example.