Elastic-plastic Fracture Behavior Research Articles

A phase field method for predicting hydrogen-induced cracking on pipelines

An accurate determination of the threshold conditions to initiate cracks on aged hydrogen pipelines is paramount for ensuring energy transport safety. In this work, a finite element-based phase field method was developed to assess the crack initiation on dented pipelines while considering the hydrogen (H) impact. Theoretical and multi-physics numerical formulas were derived for prediction of the elastic-plastic fracture behavior of H-contained steel. A critical phase field parameter, ϕ=0.69, is defined for predicting crack initiation at the dent on pipelines. The presence of H within the steel decreases the threshold dent depth for initiating H-induced cracks. When the initial H concentration increases from 0 to 0.5 wppm, the maximum dent depth for crack initiation reduces from 17.5 mm to 10.7 mm. The maximum dent depth required for crack initiation reduces from 17.5 mm to 7.8 mm when an internal pressure of 8 MPa is applied on the steel pipe. The site with the maximum phase field parameter changes during indentation, implying that the location initiating cracks depends on the dent dimension. The existing criteria in ASME B31.12 standard are not applicable for predicting H-induced crack initiation on dented pipelines. This study proposes a new method to predict hydrogen-induced cracking on aged pipelines when transporting hydrogen.

Investigation on the fracture behavior of octet-truss lattice based on the experiments and numerical simulations

Octet-truss lattice is an excellent carrier for structure–function integration because of its natural porous characteristics and remarkable bearing capacity. Currently, a significant discussion in its engineering applications revolves around assessing the fracture toughness of the lattice structure. In this paper, the single edge notched bend (SENB) specimens composed of PolyMaxTMPLA with shallow crack are prepared using the Fused Deposition Modelling (FDM) method, and three-point bending tests are conducted to investigate the fracture behavior of the octet-truss lattices. Based on the elastic–plastic fracture behavior of the specimens, the J-integral method is used to calculated the effective fracture toughness and the effect of shallow crack on the fracture toughness was considered. The experimental results show that the effective fracture toughness of the polymer specimens increases linearly with the relative density and the square root of truss length. To study the fracture behavior of lattice structure deeply, the numerical simulations are performed to further analyze the fracture behavior of the structures and verified by the experimental results. The results suggest that the fracture at the nodes and the truss near the nodes is the main failure mode of the specimens. Specially, the truss in the X-Z plane always breaks before the X-Y plane, while the deformation of truss in the Y-Z plane is always elastic. A prediction formula of the effective fracture toughness of 3D printed PLA polymer octet-truss lattice is determined based on a non-dimensional parameter sensitive to the loading mode.

A fatigue crack growth prediction model for cracked specimen under variable amplitude loading

The objective of this study was to propose a crack growth prediction model for cracked specimens under large and variable amplitude loading conditions. In this study, the concept of change in net-section strain energy was applied to simulate elastic–plastic fracture behavior, and three-dimensional fitting of the results with respect to changes in the net-section strain energy, load ratio, and crack growth rate was performed to create the crack growth prediction model. The validity of the generated model was examined using comparisons with experimental data as well as simulation results from existing crack growth models under several variable loading conditions.

Assessment of Elastic-Plastic Fracture Behavior of Cortical Bone Using a Small Punch Testing Technique.

The fracture properties of cortical bone are directly coupled to its complex hierarchical structure. The limited availability of bone material from many anatomic locations creates challenges for assessing the effect of bone heterogeneity and anisotropy on fracture properties. The small punch technique was employed to examine the fracture behavior of cortical bone in terms of area under the curve values obtained from load-load point displacement behavior. Fracture toughness of cortical bone was also determined in terms of J-toughness values obtained using a compact tension (CT) test. Area under the curve values obtained from the small punch test were correlated with the J-toughness values of cortical bone. The effects of bone density and compositional parameters on area under the curve and Jtoughness values were also analyzed using linear and multiple regression analysis. Area under the curve and J-toughness values are strongly and positively correlated. Bone density and %mineral content are positively correlated with both area under the curve and J-toughness values. The multiple regression analysis outcomes support these results. Overall, the findings support the hypothesis that area under the curve values obtained from small punch tests can be used to assess the fracture behavior of cortical bone.

Elastic-plastic delamination of multilayered graded four-point bending beam

PurposeThis paper aims to analyze the elastic-plastic delamination fracture behaviour of multilayered functionally graded four-point bending beam configuration.Design/methodology/approachThe mechanical response of beam is described by a power-law stress-strain relation. The fracture is studied analytically in terms of the strain energy release rate by considering the beam complimentary strain energy. The beam can have an arbitrary number of layers. Besides, each layer may have different thickness and material properties. Also, in each layer, the material is functionally graded along the beam width. A delamination crack is located arbitrary between layers. Thus, the crack arms have different thickness.FindingsThe analysis developed is used to elucidate the effects of crack location, material gradient and non-linear behaviour of material on the delamination fracture. It is found that the material non-linearity leads to increase in the strain energy release rate. Therefore, the non-linear behaviour of material should be taken into account in fracture mechanics-based safety design of structural members and components made of multilayered functionally graded materials. The analysis revealed that the strain energy release rate can be effectively regulated by using appropriate material gradients in the design stage of multilayered functionally graded constructions.Originality/valueDelamination fracture behaviour of multilayered functionally graded four-point bending beam configuration is studied in terms of the strain energy release rate by taking into account the material non-linearity.

301L搭接激光焊接接头拉伸过程的弹塑性演变及断裂数值分析

301L搭接激光焊接接头拉伸过程的弹塑性演变及断裂数值分析

Size-dependent fracture toughness of tungsten

In order to understand the size-dependent fracture behaviour of tungsten at the microscale, micro-cantilever tests were performed on single crystalline and ultrafine grained tungsten. The elastic-plastic fracture behaviour and crack tip plasticity were found to be strongly influenced by the sample size. The smallest cantilevers with dimensions below one micron failed by pure cleavage fracture at a fracture toughness of 1.5 MPa m1/2, which agrees well with the Griffith theory for brittle fracture. With increasing specimen size crack tip plasticity was observed, leading to a successive increase in fracture toughness and crack resistance behaviour. Using scanning transmission electron microscopy and electron backscatter diffraction, dislocation densities were analysed and measured. Pronounced plastic strain gradients were found at the crack tip for an intermediate specimen size, which also showed the highest crack resistance. When further increasing the specimen size, large plastic zones were still observed but the gradients in plastic strain vanished, leading to a reduction in the crack resistance behaviour. For those samples, a size independent fracture toughness of ca. 7 MPa m1/2 was found, which is close to macroscopic literature data. Increasing the initial dislocation density in the single crystals through plastic pre-straining led to a reduced stable crack growth behaviour but did not affect the fracture toughness. Furthermore, the effect of grain boundaries on the fracture behaviour was studied by means of ultrafine grained tungsten. A fracture toughness lower than the one reported in literature was found, which is explained by the higher susceptibility to failure once a crack propagates at the micro-scale.

On Elastic-Plastic Fracture Behavior of a Half-Space Under Prescribed Loading

The plastic zones at crack tips play a significant role in fracture behaviors of materials. In this paper, a semi-analytic solution is proposed for the plastic zone size of cracks in an elastic-perfectly plastic half-space under prescribed loading. This solution also considers the subsurface stress distribution influenced by the plastic zones at crack tips. The cracks can be treated as a distribution of edge dislocations with unknown densities by using the distributed dislocation technique. In order to calculate the plastic zone sizes of crack tips, two stripes ahead of crack tips are introduced as plastic zones based on the Dugdale model of small scale yielding. The numerical values can be determined by canceling the stress intensity factor due to the closure stress and that due to the applied load. It is noted that the plastic zone sizes are affected by the crack length and depth, yield strength of substrates and loading conditions.

The interface effect of a nano-inhomogeneity on the fracture behavior of a crack and the nearby edge dislocation

The interface effect of a nano-inhomogeneity on the elastic–plastic fracture behavior of a crack with the influence of nearby edge dislocation is studied by applying the surface/interface stress model. When the inhomogeneity and the crack become nano-sized, the bimaterial interface contributes considerable stresses to the crack surfaces, which are usually ignored in the traditional micro/macro crack problems. With the existence of nano-inhomogeneity, an extra dislocation near the crack may be either absorbed into the crack (so the crack grows bigger) or repelled away by the crack and the inhomogeneity. The Zener–Stroh mechanism is employed to model the nano-sized fracture behavior and the generalized Irwin plastic zone correction is taken to improve the fracture analysis at the crack tips. Using the complex potential functions and distributed dislocation method, the stress intensity factor, plastic zone size, and crack tip opening displacement are evaluated by solving the Cauchy singular integral equations. The numerical examples prove that the values of stress intensity factors, plastic zone size and crack tip opening displacement are sensitive to the interface properties of the current nano-scaled problem, especially when the inhomogeneity is small. When the extra edge dislocation is close to the sharp crack tip, the stress intensity factor increases significantly, which indicates the crack has a potential to absorb the nearby dislocation. Further investigations find that mixed mode loading conditions always induce much higher stress intensity factors, plastic zone size, and crack tip opening displacement comparing to pure mode I loading problem.

Small scale yielding analysis for a disclination-nucleated Zener-Stroh crack interacting with a circular inclusion

The elastic-plastic fracture behavior of a Zener-Stroh crack nucleated by a wedge disclination dipole interacting with a nearby circular inclusion is investigated. It is known that a disclination is a strong source of internal stresses and energy, one possible way for the relaxation of the stresses can be in the form of an initiated crack. In the current work, the nucleated Zener-Stroh crack is simulated by a series of edge dislocations with distributed dislocation method. The influence of the disclination is accounted through crack surface traction free condition. To improve the analysis accuracy, the Irwin plastic zone correction is employed to evaluate the elastic-plastic fracture behavior at the sharp crack tip. Von Mises yielding criterion is applied in the plastic zone area to judge the yielding occurrence. Numerical results are given to study the influence of the disclination strength, disclination dipole arm as well as material properties on the stress intensity factor (SIF), plastic zone size (PZS), and crack tip opening displacement (CTOD). It is found that the property of the wedge disclination dipole has great effect on the stress field and the elastic-plastic fracture behavior of the Zener-Stroh crack. Either disclination strength or dipole arm increases, the SIF, PZS, and CTOD will increase significantly. For the same disclination, if the nucleated Zener-Stroh crack has a longer crack length, the SIF, PZS, and CTOD could be smaller. For a Zener-Stroh crack nucleated between the inclusion and the disclination dipole, the interaction between the disclination and inclusion greatly influences the elastic-plastic fracture behavior. However, this influence highly depends on material combinations of the two phases.

Plastic zone correction on a Zener–Stroh crack interacting with a circular inclusion in ductile materials

AbstractElastic–plastic stress analysis on a matrix Zener–Stroh crack interacting with a circular inclusion (fibre) in fibre‐reinforced composites has been carried out. The Zener–Stroh crack is initiated near the fibre in the pure matrix. Plastic zone correction is introduced the first time for such a crack–inclusion interaction problem so that the fracture behaviour can be analysed more accurately. To determine the plastic zone sizes, a generalized Irwin model is proposed for the mixed‐mode problem where the Von Mises stress yielding criterion is employed. Different to a Griffith crack, a Zener–Stroh crack propagation always occurs from the sharp tip whose relative position to the inclusion has great effect on the elastic–plastic fracture behaviour of the crack. In our study, the plastic zone size (PZS), crack tip opening displacement (CTOD) and effective stress intensity factor (SIF) are evaluated by solving the formulated singular integral equations. Through the numerical examples, the influence of the inclusion (fibre) shear modulus, crack–inclusion distance and the crack sharp tip position on the fracture behaviour of the crack is discussed. It is found that the shear modulus ratio and the crack–inclusion distance have great effect on the normalized values of PZS and CTOD, but the effects highly depend on the crack sharp tip position.

A Zener–Stroh crack interacting with a coated inclusion with generalized Irwin plastic zone correction

The elastic–plastic fracture behavior of a Zener–Stroh crack interacting with a coated inclusion in composite materials has been investigated with crack tip plastic zone corrections. With the distributed dislocation method, the crack problem is formulated into a set of singular integral equations which are solved numerically. The plastic zone sizes at the both crack tips are determined by a generalized Irwin model where Von Mises stress yielding criterion is used. The stress intensity factor (SIF), the plastic zone size (PZS), the crack tip opening displacement (CTOD) and the effective stress intensity factor have been evaluated. In the numerical examples, the influence of the inclusion shear modulus, the coating-layer thickness and shear modulus, as well as the distance between the crack and inclusion, on the SIF, the PZS and the CTOD are discussed in detail. Numerical examples show that increasing the shear modulus or the thickness of the coating phase, the influence of the inclusion on the normalized SIF and the normalized PZS will be shielded.

Effect of Characteristic Lengths of Fracture on Thermal Crack Patterns

AbstractApproximately uniformly spaced cracking occurs in many different materials and processes during thermal or drying shrinkage. Such cracks may occur when a slab of material restrained at the bottom is subjected to a sudden reduction in temperature at the top. Previous research indicates that the crack patterns obtained depend on the Griffith crack length for a shrinking solid. This paper shows that for materials exhibiting elastic-plastic fracture behavior, the fracture energy, Young’s modulus, and tensile strength in combination form a second characteristic length of fracture of the material that has a significant impact on the cracks formed.

On elastic–plastic fracture behavior of a bi-layered composite plate with a sub-interface crack under mixed mode loading

A generalized Irwin model is proposed to investigate elastic–plastic fracture behavior of a bi-layered composite plate with a sub-interface crack under combined tension and shear loading. The dependence of the stress intensity factors, the plastic zone size, the effective stress intensity factor and the crack tip opening displacement on the crack depth h, the Dundurs’ parameters and the phase angle θ is discussed in detail. Numerical results show that in most cases, if the crack is embedded in a stiffer material, when the crack is close to the interface, the plastic zone size and the crack tip opening displacement will increase. On the contrary, if the crack is embedded in a softer material, when the crack is close to the interface, the plastic zone size and the crack tip opening displacement will decrease.

Elastic–plastic fracture behavior of a radial matrix crack interacting with a circle inclusion with generalized Irwin corrections

A generalized Irwin plastic zone model is proposed to investigate the interaction problem for a circular inclusion embedded in an elastic–plastic matrix that contains a radial crack, oriented at an arbitrary angle from a remote load. The distributed dislocation technology is applied to formulate the current problem. The effective stress intensity factors, the plastic zone size, and the crack tip opening displacement are evaluated by solving the formulated singular integral equations. In the numerical examples, the inclusion is taken as a void and a rigid body. The effects of the crack angle and the inclusion–crack distance (the distance from the inclusion center to the crack center) on the effective stress intensity factors, the plastic zone size, and the crack tip opening displacement are discussed in detail. Numerical results show that if the crack angle is not large, the values of the plastic zone size and the crack tip opening displacement are less than the corresponding values in the homogenous case when the inclusion is a rigid body; when the inclusion is a void, these values are larger than the corresponding values in the homogenous case.

On the Plastic Zone Size and the Crack Tip Opening Displacement of an Interface Crack Between two Dissimilar Materials

In the paper, the elastic-plastic fracture behavior of an interface crack between two dissimilar materials is investigated. The mixed-mode Dugdale model is applied to examine the plastic zone size and the crack tip opening displacement. In numerical examples, the plastic zone size and the crack tip opening displacement of an interface crack under uniform loads are studied in detail. Two formulae are proposed to calculate the plastic zone size and the crack tip opening displacement of an interface crack under small scale yielding conditions.

Estimation of the Elastic-Plastic Fracture Behavior of Fiber Reinforced MMC According to the Change of Interfacial Characteristics

Fiber reinforced metal matrix composites (MMCs) are recently used in automobile, ship, aerospace and manufacturing industry because they have high stiffness and strength. The effective utilization of the strength and stiffness of the fiber reinforced MMCs depends on efficient load transfers from the matrix to fibers through the interfacial region. However, during the fabrication and afterward utilization of composites, so many numbers of micro crack may extend, especially at the interface, even before any load has been applied. Thus, in this study, the interfacial stress state and behavior of the interfacial perpendicular crack for transversely loaded unidirectional fiber reinforced MMCs investigated by using the elastic-plastic finite element analysis.

A Study on Estimation of the Pipe Fracture Characteristics

In order to analyze the elastic-plastic fracture behavior of a structure, the fracture resistance curve of the material should be known. However, it is difficult to evaluate the fracture characteristics with an experiment on the piping system. Instead, the fracture toughness obtained from standard specimen tests is used to analyze the structure and assess the fracture characteristics of the total structure. It is known that toughness data from the standard specimen test are conservative to predict fracture behavior of the real piping. Thus the fracture resistance curve by the fracture test of the real scaled pipe specimen would be applied to the integrity evaluation for the piping system. However, it is not only difficult to perform but also very expensive to perform full-scale pipe tests. The objective of this thesis is to propose a method to estimate the fracture resistance curve of a pipe from the result of standard specimen fracture test. To estimate the fracture resistance curve for a pipe specimen, load – load-line displacement records of a standard specimen were transformed to those of the pipe specimen. The load ratio method was proposed in order to calculate the crack length from load – crack mouth opening displacement records for the pipe specimen. To prove the validity of this estimation results, fracture tests for pipe specimens were performed. Consequently the applicability of the proposed method was investigated by comparing estimated results with tested results.

A Study on the Evaluation of Pipe Fracture Characteristics

In order to analyze elastic-plastic fracture behavior of a structure, the materials fracture resistance curve should first be determined. The standard CT specimen was used to obtain fracture resistance curves of a piping system. However, this is known to be very conservative in evaluating the integrity of a structure. In addition, the specimen geometry and dimension due to the constraint effect alters the fracture resistance curve. The objective of this paper is to verify the conservativeness of the fracture resistance curve by the standard CT specimen, subsequently to provide an additional safety margin. To this end, the fracture tests using a real pipe specimen and the standard CT specimen tests were performed. The 4-point bending test method was applied in the pipe test while the direct current potential drop method was used to measure the pipe's crack extension and length. Finite element analyses for J-Q analyses were performed with CT specimens and pipes in order to prove the additional safety margin. From these test results and analyses of both pipe and the standard CT specimen, it was observed that the fracture analysis with the standard CT specimen is conservative and the additional safety margin was proved.

실배관 파괴특성 평가에 관한 연구

In order to analyze the elastic-plastic fracture behavior of a structure, the fracture resistance curve of the material should be known first. The standard CT specimen was used to obtain the fracture resistance curves of a piping system. However, it is known that the fracture resistance curve by the standard CT specimen is very conservative to evaluate the integrity of a structure. Also the fracture resistance curve is effected by the specimen geometry and the dimensions because of the constraint effect. The objective of this paper is to be certain the conservativeness of the fracture resistance curve by the standard CT specimen and to provide an additional safety margin. For these, the fracture tests using a real pipe specimen and to provide an additional safety margin. For these, the fracture tests using a real pipe specimen and the standard CT specimen test were performed. A 4-point bending jig was manufactured for the pipe test and the direct current potential drop method was used to measure the crack extension and the length for the pipe test. Also finite element analyses were performed with a CT specimen and a pipe in order to prove the additional safety margin. From the result of tests and analyses of the pipe and the standard CT specimen, it was observed that the fractrue analysis with the standard CT specimen is conservative and the additional safety margin was proved.