Crack Tip Stress Distribution Research Articles

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.

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.

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.

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.

Deformation inhomogeneity at the crack tip of polycrystalline copper

Molecular dynamics simulation is conducted on single crystal and polycrystalline copper. Two different crack tip orientations (001) [-110] and (001) [010] are selected for copper single crystal. For copper single crystal with crack tip orientation of (001) [010], stress is concentrated at the crack tip, and cleavage crack propagation happens due to lack of dislocation activity at the crack tip. For copper single crystal with crack tip orientation of (001) [-110], continuous emission of dislocations from crack tip results crack tip blunting and reduction of stress concentration as well. Homogeneous crack tip stress and strain fields are evident for copper single crystals, however, stress and strain fields slightly alter with the generation of dislocations and defects. Crack tip stress and strain distribution are inhomogeneous from the beginning of the deformation for polycrystalline copper. Higher stress concentration at the grain boundary than crack tip results in nucleation of initial dislocations from the grain boundary during plastic deformation.

Characterizing dynamic crack-tip stress distribution and evolution under blast gases and reflected stress waves by caustics method

Blast gases and reflected stress waves are crucial in the blast fracturing process. Characterizing dynamic crack-tip stress distribution and evolution under these two loadings is difficult due to challenges in visualizing blast-induced cracks, gases, and stress waves simultaneously and the subsequent interpretation. This paper presents an optical caustics method with high-speed photography to visualize gases and reflected stress waves and capture the caustics pattern in the crack tip, using a PMMA plate (400 mm × 300 mm × 5 mm) subjected to the explosion of lead azide (120 mg). And then a modified analytical model was proposed to reproduce experimental results and extract stress intensity factors (SIFs) more precisely than the classical caustics interpretation. Finally, fracture surface was examined by a light microscope. Crack-tip stress distribution and evolution are indicated by the shape and size of the caustics pattern, respectively. The classical (circle) caustics pattern under gases indicates K-dominated stress field in the crack tip, while the distorted (ellipse) caustics pattern under reflected stress waves implies K-dominated stress field is violated. By the modified SIFs measurement, it is found that SIFs under gases decrease and produce bigger and sparser micro cracks on the fracture surface, while SIFs increase under reflected stress waves with a higher loading rate and cause smaller and denser micro cracks. Based on the change of micro cracks, the curved crack front is identified in the transition of gas and reflected stress wave loadings. This paper shows that caustics method can visualize and precisely characterize crack-tip stress field under quasi-static loading of blast gases and transient loading of reflected stress waves.

Effects of stop hole on crack turning, residual fatigue life and crack tip stress field

The aim of this paper is to research the effects of stop hole on crack turning, residual fatigue life and crack tip stress field, in which the location, size and shape of stop hole are considered. The numerical model is established according to M-integral technology, and crack turning angle is determined by maximum hoop stress criterion. The calculation results show that stop hole location has a significant effect on crack turning angle and residual fatigue life, and it should be drilled with a reasonable distance in vertical and horizontal direction around crack tip to achieve a better residual fatigue life retardation effect. The larger the stop hole size is, the wider effect range of stop hole on crack turning and residual fatigue life will be. The effects of elliptical stop hole on crack turning angle and residual fatigue life retardation are greater than that of round hole when the distance in vertical direction increases. Crack tip stress distribution is changed by increasing σy and decreasing σx, and the most dramatical changes occur at the circumferential direction of 90° and 270°.

Improved crack analysis of two-dimensional functionally graded materials by enriched natural element method

The numerical calculation of stress intensity factors of two-dimensional functionally graded materials is introduced by an enriched Petrov–Galerkin natural element method (enriched PG-NEM). The overall trial displacement field is basically approximated in terms of Laplace interpolation functions and it is enriched by the near-tip asymptotic displacement field. The overall strain and stress fields which were approximated by PG-NEM were smoothened and enhanced by the patch recovery. The modified interaction integral [Formula: see text] is used to evaluate the stress intensity factors of functionally graded materials with the spatially varying elastic modulus. The validity of present method is justified through the evaluation of crack-tip stress distributions and the stress intensity factors of four numerical examples. It has been found that the proposed method effectively and successfully captures the near-tip stress singularity with a remarkably improved accuracy, even with the remarkably coarse grid, when compared with an extremely fine grid and the analytical and numerical reference solutions.

2-D Reliable Crack Analysis by Enriched Petrov-Galerkin Natural Element Method

This paper introduces a 2-D enriched Petrov-Galerkin natural element method (enriched PG-NEM) for the reliable crack analysis. The total displacement is expressed as a linear combination of usual non-singular displacement field and the near-tip singular one. The former is approximated in terms of Laplace interpolation functions, and its strain and stress distributions are smoothened by the patch recovery technique. The unknown coefficients of the latter are determined by a coupled PG-NEM, and its strain and stress distributions are smoothened by the patch recovery technique. The validity of present method is justified through the evaluation of crack-tip stress distributions and the stress intensity factors (SIFs) through two numerical examples. It has been found that the proposed method effectively and successfully captures the near-tip stress singularity with the reasonable accuracy, even with the remarkably coarse grid, when compared with an extremely fine grid and the analytical and numerical reference solutions.

Compilation and Application of UMAT for Mechanical Properties of Heterogeneous Metal Welded Joints in Nuclear Power Materials

For the problem of mechanical properties of heterogeneous dissimilar metal welded joints, when analyzed by the finite element method, it is usually simplified into a “sandwich” material structure model. However, the mechanical properties of materials in different regions of the “sandwich” material mechanics model are different, and there will be mutations at the material interface. In order to accurately describe the mechanical properties of welded joints, the constitutive equations of dissimilar metal welded joint materials were compiled, and the constitutive equations of inhomogeneous materials whose material mechanical properties were continuously changed with space coordinates were established. The ABAQUS software was used to establish the “sandwich” model and the continuous transition model. The model is used to compare and analyze the crack tip stress distribution of different yield strength mismatch coefficients. The results show that the continuous transition material model eliminates the mutation of the “sandwich” model at the material interface and achieves the continuous change of the mechanical properties of the material. For the longitudinal crack, under the influence of different mismatch coefficients, the crack tip stress field of the transitional material model is deflected toward the low yield strength side. The compilation of constitutive equations for continuous transition materials of dissimilar metal welded joints provides a basis for the safety evaluation of dissimilar metal welded joints.

A new semi-analytical approach for obtaining crack-tip stress distributions under variable-amplitude loading

Near threshold fatigue crack response is extremely sensitive to load history. It is associated with the influence of near-tip stress on instantaneous resistance of crack tip surface layers to failure under atmospheric conditions. The paper deals with computational aspects of stress and strain distributions at the crack tip. A new approach is proposed to obtain near-tip stress under variable amplitude loading. The method considers a combination of standard rules for determining local strains (Linear rule, Neuber rule, ESED method, etc.) and well-known in Finite Element Analysis (FEA) return mapping algorithm in context of nonlinear mixed hardening material model. Iterative procedure based on Newton-Raphson method is proposed to calculate plastic variables and near-tip stress at each load step. The calculated results obtained by new model are validated with the traditional approach in case of Al2024-T3 alloy for constant amplitude loading after tensile/comprehensive overloads.

Fracture Toughness Prediction under Compressive Residual Stress by Using a Stress-Distribution T-Scaling Method

The improvement in the fracture toughness Jc of a material in the ductile-to-brittle transition temperature region due to compressive residual stress (CRS) was considered in this study. A straightforward fracture prediction was performed for a specimen with mechanical CRS by using the T-scaling method, which was originally proposed to scale the fracture stress distributions between different temperatures. The method was validated for a 780-MPa-class high-strength steel and 0.45% carbon steel. The results showed that the scaled stress distributions at fracture loads without and with CRS are the same, and that Jc improvement was caused by the loss in the one-to-one correspondence between J and the crack-tip stress distribution. The proposed method is advantageous in possibly predicting fracture loads for specimens with CRS by using only the stress–strain relationship, and by performing elastic-plastic finite element analysis, i.e., without performing fracture toughness testing on specimens without CRS.

Comparison of constraint analyses with global and local approaches under uniaxial and biaxial loadings

Abstract Fracture toughness is an important material property used to perform the integrity assessment of engineering components containing cracks. Due to the difference in crack tip constraint, specimens may show different fracture toughness. The constraint difference for cruciform specimen with shallow crack, compact tension (CT) specimen and three point bending specimen with shallow and deep cracks are investigated. Both linear elastic and elastic-plastic fracture mechanics are applied to study the constraint effect based on two-parameter fracture criterion . Crack tip constraint depends on the applied loading. J-A 2 method is used to precisely capture the crack tip constraint and crack tip stress distributions. Local approach to fracture can be applied to transfer the fracture toughness among different specimens under uniaxial and biaxial loadings . In case of positive T -stress, T-stress increases with KI. In the case of negative T-stress, T-stress decreases with KI. Q-stress generally decreases with applied loading for both deep crack and shallow crack cases. Loss of constraint occurs for the single-edged bending (SEB) specimen with deep crack and thus raises the question whether the SEB specimen is proper to be used to obtain material toughness. For the cruciform bending (CRB) specimen, the constraint at the crack tip surface shows a least constraint while the deepest point has a relatively higher constraint. At a fracture probability of 10%, the fracture toughness difference between CT specimen and CRB specimen is about 50 MPa m0.5, i.e 200% of the fracture toughness. This big difference demonstrates the importance of considering the constraint effects in the integrity analysis.

T-scaling method for stress distribution scaling under small-scale yielding and its application to the prediction of fracture toughness temperature dependence

In this paper, a new method for scaling the crack-tip stress distribution under small-scale yielding conditions is proposed and named the T-scaling method. This method enables identification of the different stress distributions for materials with different tensile properties but identical load in terms of K or J. Then, by assuming that the temperature dependence of a material is represented by the stress-strain relationship temperature dependence, a method to predict the fracture load at an arbitrary temperature from the already known fracture load at a reference temperature is proposed. This method is combined with the T-scaling method and the knowledge that the “fracture stress for slip induced cleavage fracture is temperature independent.” Once the fracture load is assumed, the fracture toughness Jc at the temperature under consideration can be evaluated by running elastic-plastic finite element analysis. Finally, the above-mentioned framework for predicting the Jc temperature dependence of a material in the ductile-to-brittle temperature region was validated for 0.55% carbon steel JIS S55C and reactor pressure vessel steel A533B. The proposed framework seems to be able to solve the problem faced by the master curve in the relatively high temperature region by requiring only tensile tests.

応力分布Tスケーリング法適用による圧縮残留応力付与時破壊靭性値の予測

The fracture toughness Jc of the material in the ductile to brittle transition temperature (DBTT) region shows test specimen thickness (TST) effect and temperature dependence, and apparently increases when compressive residual stress is applied. In this paper, as TST effect and temperature dependence, the fact that Jc apparently increases due to compressive residual stress is attributable to the loss in the one-to-one correspondence between J and the crack-tip stress distribution, and then, the fracture prediction of the specimen with compressive residual stress was performed using the T-scaling method proposed by the authors, and its validity was confirmed for high strength steel of 780 MPa class and 0.45 % carbon steel JIS S45C. In addition, it was suggested that the minimum of Jc with compressive residual stress can be predicted by requiring only the tensile test.

小規模降伏条件下応力分布スケーリング法の提案と破壊靭性値の温度依存性予測への適用

In this paper, a new method for scaling the crack tip stress distribution under small scale yielding condition was proposed and named as T-scaling method. This method enables to identify the different stress distributions for materials with different tensile properties but identical load in terms of K or J. Then by assuming that the temperature dependence of a material is represented as the stress-strain relationship temperature dependence, a method to predict the fracture load at an arbitrary temperature from the already known fracture load at a reference temperature was proposed. This method combined the T-scaling method and the knowledge “fracture stress for slip induced cleavage fracture is temperature independent.” Once the fracture load is predicted, fracture toughness Jc at the temperature under consideration can be evaluated by running elastic-plastic finite element analysis. Finally, the above-mentioned framework to predict the Jc temperature dependency of a material in the ductile-to-brittle temperature distribution was validated for 0.55% carbon steel JIS S55C. The proposed framework seems to have a possibility to solve the problem the master curve is facing in the relatively higher temperature region, by requiring only tensile tests.

Dynamic Strain Evolution around a Crack Tip under Steady- and Overloaded-Fatigue Conditions

We investigated the evolution of the strain fields around a fatigued crack tip between the steady- and overloaded-fatigue conditions using a nondestructive neutron diffraction technique. The two fatigued compact-tension specimens, with a different fatigue history but an identical applied stress intensity factor range, were used for the direct comparison of the crack tip stress/strain distributions during in situ loading. While strains behind the crack tip in the steady-fatigued specimen are irrelevant to increasing applied load, the strains behind the crack tip in the overloaded-fatigued specimen evolve significantly under loading, leading to a lower driving force of fatigue crack growth. The results reveal the overload retardation mechanism and the correlation between crack tip stress distribution and fatigue crack growth rate.

Finite element simulations of notch tip fields in magnesium single crystals

Recent experiments using three point bend specimens of Mg single crystals have revealed that tensile twins of {10 (1) over bar2}-type form profusely near a notch tip and enhance the fracture toughness through large plastic dissipation. In this work, 3D finite element simulations of these experiments are carried out using a crystal plasticity framework which includes slip and twinning to gain insights on the mechanics of fracture. The predicted load-displacement curves, slip and tensile twinning activities from finite element analysis corroborate well with the experimental observations. The numerical results are used to explore the 3D nature of the crack tip stress, plastic slip and twin volume fraction distributions near the notch root. The occurrence of tensile twinning is rationalized from the variation of normal stress ahead of the notch tip. Further, deflection of the crack path at twin-twin intersections observed in the experiments is examined from an energy standpoint by modeling discrete twins close to the notch root.

Review: Progress in the Studies on Mechanical Properties of Materials

Materials science and engineering is one of the hot research topics in the world, among which mechanical properties of materials play a critical role in application of the new materials. Based on this, a special session Mechanical Properties of Materials was held within the 2nd Global Conference on Materials Science and Engineering, Nov. 20-22, 2013. This special issue contains a selection of twenty scientific papers, which are focused on the structure, mechanical properties, and strength of materials. In this review, the selected papers from the special session are summarized. Introduction. The Global Conference on Materials Science and Engineering (CMSE) is an annual event since 2012. The CMSE 2013 was held by Hubei University of Science and Technology in the City of Xianning (Hubei, China), November 20-22, 2013. Within this event, a special session named Mechanical Properties of Materials was held. In this session, 31 papers were selected for publication, of them 20 papers are published in this special issue (1-20), two more (21, 22) in the next issue, and 9 papers are published by Materials Research Innovations (23-31). All papers underwent the standard peer-review process of the journal and were accepted for publication based on the evaluation of at least two independent anonymous reviewers. Highlighted Papers. Results of the study (1) indicate that crack tip stress distribution characteristics and crack propagation dynamics are closely related to the microstructure evolution caused by the change of a strain rate and temperature. At a lower strain rate and temperature, the crack propagated by a brittle mechanism without the change in atomic configuration near the crack tip. The stress concentration occurred at the crack tip of a growing crack. The crack propagation exhibited a gradual brittle-to-ductile transition with increasing temperature and strain rate, the peak stress was accompanied by the appearance of the microstructure evolution ahead of the crack tip. In (3), uniformly distributed TiC nanoparticle-reinforced iron-based composites were successfully prepared by planetary milling in argon and subsequent hot pressing. Nearly full density composite specimens could be obtained via milling for 6 h followed by hot pressing at 1100C under 50 MPa. Comparatively spherical TiC particles and fine fibrous Fe3C phases were observed in the iron matrix composite. Microstructural analysis results show that the average diameter of TiC particles and the length of Fe3C phases tend to decrease with an increase in the TiC volume content. Her and Wu (7) studied the annealing effect on the microstructure and mechanical properties of titanium nitride (TiN) films. Atomic force microscopy analysis demonstrated that surface roughness of TiN films decreased from 3.83 to 2.43 nm as the annealing temperatures increased from 100 to 300C. Atomic force microscopy image of