Crack Tip Area Research Articles

A crack-tip element for modelling arbitrary crack propagations

Numerical study on crack propagation are of great importance for structure design and assessment. In this contribution, the floating node method (FNM) is combined with the symplectic analytical singular element (SASE) to form a new crack-tip element. The four node quadrilateral crack-tip element contains a SASE for the crack tip area to account for the singularity issue. Floating nodes are used to form a smooth transition mesh to full fill the other area of the element automatically once the SASE has been generated. Delaunay triangulation is used to guarantee the quality of the transition elements. Strong discontinuity resulted from complex crack networks with multiple cracks is treated by the FNM. Criteria for crack nucleation, propagation angle and length of new crack segment are given. Interaction between cracks and between crack and defect can be readily modelled without any prior knowledge of crack path. The fracture process of crack propagation can be modelled without remeshing. Inherited from the FNM, the proposed crack-tip element is especially suitable to be implemented in the form of a user defined element. Completed fracture processes with crack nucleation, propagation and interaction are modelled in the numerical examples.

Influence of Yield Stress Mismatch on the Creep Stress Field around Crack Tip of Stress Corrosion Cracking

To understand the influence of yield stress mismatch on the creep stressfield around crack tip in safe-end dissimilar metal welded joints at primary circuit, the influences of different mismatch coefficients on the creep stress field around the crack front were analyzed using ABAQUS software. Results show thatthe Mises stress distribution is not very different after the creep under different mismatch coefficients.The equivalent plastic strain(PEEQ) in the Nickel based 182 near crack tip is basically remain unchanged and the PEEQ of HAZ is decreasing with the increasing of the mismatch coefficient.The creep strain is mainly concentrated in the crack tip area and there is little change in creep strain under different mismatch coefficients.

The thermal shock resistance prediction of porous ceramic sandwich structures with temperature-dependent material properties

A general numerical model to predict the thermal shock resistance of porous ceramic sandwich (PCS) structures with temperature-dependent material properties is developed. Knowledge of the temperature distribution and associated thermal stress in PCS panel is determined by the finite element method of coupled thermoelasticity. The present work considers the hot/cold shock induced center/edge cracks and measures the time-varied thermal stress intensity factors at the crack tip area. The roles of crack length, relative density of foam core, thermal shock load and geometric parameters of the PCS structures are examined. Moreover, fracture failure analysis of the whole PCS structures is carried out and crack propagation manners are detected. The thermal shock resistance curves of the structures are provided and the critical thermal shock temperatures are estimated for any selected characteristic materials. Results reveal that the thermal shock resistance of the PCS structures will be dramatically underestimated with the ignorance of temperature-dependent material properties. The analysis model of this paper provides a rapid prediction of thermal shock behavior of PCS structures at arbitrary temperatures.

Multi-scale study of the deformation mechanisms of thermoelectric p-type half-Heusler Hf0.44Zr0.44Ti0.12CoSb0.8Sn0.2

Increasing the figure of merit ZT of thermoelectric (TE) alloys is a challenge that is currently attempted through various metallurgy methods, including nanostructuring and dislocation engineering. Microstructures with such a level of complexity raise questions about the mechanical reliability of these new materials. Indeed, despite the values of hardness and elastic modulus known for the clear majority of TE materials, the data on deformation mechanisms are still rare. Focusing on the nanostructured p-type half-Heusler Hf0.44Zr0.44Ti0.12CoSb0.8Sn0.2, our multi-scale study aims to analyze the deformation mechanisms. Experiments conducted at macro-, meso-, and micro-scale are designed to trigger and assess plasticity mechanisms. Compression testing on bulk samples subject to a confining pressure environment and temperature leads to an exclusive brittle failure. The mixed-mode failure mechanisms involve switching between intra- and inter-granular crack propagation, depending on the grain size met by the crack tip. Cube-corner nanoindentation at meso-scale generates cracks and enables fracture toughness estimation, while TEM analysis of the crack tip area confirms no dislocation activity and 3D-Electron Back Scattered Diffraction technique confirms the mixed crack propagation behavior. At micro-scale, micro-pillar compression stress-strain curves and failure mechanisms are comparable with bulk samples testing analysis. These results can be used to provide design guidelines for more crack-resistant TE alloys.

Numerical simulation of a heat generation in a layered material during ultrasonic wave propagation

Ultrasonic vibrothermography is an effective and non-destructive method, which can be used for a quick detection of coating defects on large surfaces. Mechanical excitation of a layered structure induces inelastic deformation and, as a consequence, energy dissipation in the defective area and local heating. In this work, a three-dimensional numerical simulation of this process is applied to the bi-metallic layered structure with an edge crack. Two models of energy dissipation are considered (hysteretic damping model and visco-elastic Maxwell’s model) for simulation of energy dissipation in a crack tip area under ultrasonic loading. The models allow us to study the effects of the loading frequency, loading direction and location of the coating defects on the heat dissipation and propose optimal regimes for the ultrasonic vibrothermography of bi-metallic layered structures.

Effect of Testing Temperature on Sulfide Stress Cracking of Low Alloy Steel

In this study, effects of environmental temperature on susceptibility to sulfide stress cracking (SSC)—a type of hydrogen embrittlement (HE) occurring in sour environments—of low alloy steels were investigated from the perspective of hydrogen entry, absorption, and accumulation. SSC susceptibility was evaluated using a double cantilever beam (DCB) test and a four-point bend (4PB) test in sour environments at several testing temperatures. 4PB test specimens included notched and un-notched specimens to investigate influences of stress concentration and local stress. In the case of evaluation methods using specimens with high-stress concentration area, a decrease in testing temperature from room temperature to 4°C significantly increased SSC susceptibility. Hydrogen entry and absorption behaviors were also evaluated at several testing temperatures using a hydrogen permeation test. The hydrogen concentration at the plastic deformed area increased remarkably with decreasing testing temperature. It is considered that the influence of testing temperature is due to hydrogen concentration at the stress concentration area with plastic deformation. In a low temperature condition, the degree of hydrogen accumulation at the crack tip areas of a DCB specimen or crack initiation site of a 4PB specimen could be higher than that in a higher temperature condition. When steels are applied to low temperature conditions with H2S, a prior material evaluation reproducing both environmental temperature and actual stress condition is needed.

Crack growth rate of inclined and deflected surface-cracks in round-bar specimens of copper processed by equal channel angular pressing under cyclic loading

For low-cycle fatigued, ultrafine grained copper, processed by equal channel angular pressing, a unique crack growth direction, either inclined at 45° or perpendicular to the loading direction, was observed around the circumference of round bar specimens. In addition, the perpendicular cracks showed a 45° deflected crack face toward the center of the specimens. To clarify the growth behavior of such inclined and deflected cracks, the role of the deformation mode at the crack-tip areas was discussed in terms of the surface damage caused by cyclic stressing and the mixed-mode deformation at the crack tips. The preexistent shear-bands/shear-cracks around the crack tips and the in-plane shear-mode deformation at the crack tips assisted the formation of shallow inclined- and deep deflected-cracks. To quantitatively estimate the severity of mechanical damage at the crack tips, the comparative stress intensity factor range under combined mode I, II and III conditions were calculated. The crack growth rate along the growth direction at the surface and bottom for inclined and deflected surface-cracks was discussed in terms of the comparative stress intensity factor range.

Hydrogen-Induced Delayed Cracking in TRIP-Aided Lean-Alloyed Ferritic-Austenitic Stainless Steels.

Susceptibility of three lean-alloyed ferritic-austenitic stainless steels to hydrogen-induced delayed cracking was examined, concentrating on internal hydrogen contained in the materials after production operations. The aim was to study the role of strain-induced austenite to martensite transformation in the delayed cracking susceptibility. According to the conducted deep drawing tests and constant load tensile testing, the studied materials seem not to be particularly susceptible to delayed cracking. Delayed cracks were only occasionally initiated in two of the materials at high local stress levels. However, if a delayed crack initiated in a highly stressed location, strain-induced martensite transformation decreased the crack arrest tendency of the austenite phase in a duplex microstructure. According to electron microscopy examination and electron backscattering diffraction analysis, the fracture mode was predominantly cleavage, and cracks propagated along the body-centered cubic (BCC) phases ferrite and α’-martensite. The BCC crystal structure enables fast diffusion of hydrogen to the crack tip area. No delayed cracking was observed in the stainless steel that had high austenite stability. Thus, it can be concluded that the presence of α’-martensite increases the hydrogen-induced cracking susceptibility.

On the effect of hydrostatic stress on fatigue crack propagation

PurposeThe purpose of this paper is to study mutual interaction between von Mises equivalent and hydrostatic stresses at the crack tip area of an elastoplastic material in order to obtain critical conditions for crack propagation under fatigue loading.Design/methodology/approachA5083-H111 aluminum alloy is used to obtain a Chaboche-type constitutive equation, which is introduced in a commercial finite elements package to evaluate stress distribution at crack tip area. A simplified three-dimensional (generalized plane strain) grid is used, resulting in fast and accurate results. Numerical simulations are performed to connect crack propagation rate with various combinations of fatigue stress amplitude, initial crack length and number of loading cycles. Distance between characteristic points of stresses distribution in the crack tip area are compared to experimental fatigue crack growth rates in order to assess the validity of the present approach.FindingsIt is found that saturation of plastic strains, i.e. maximization of von Mises equivalent stress, is a prerequisite for hydrostatic stress to take a critical-maximum value, outside the plastically saturated zone. At the point of maximum hydrostatic stress brittle fracture is initiated, driving to separation of the ligament up to crack tip, without formation of new plastic strains. The length of this ligament is defined as crack propagation step, showing good agreement with experimental data.Originality/valueThe present approach seems to constitute a reasonable and adequate method for the description of fatigue crack propagation in terms of continuum mechanics, not necessitating microscopic considerations or empirical criteria lacking theoretical or physical basis. In addition, it liberates from the notion of stress intensity factors, strongly disputed beyond linear elasticity. Improved constitutive equations and numerical models are expected to drive in a complete fatigue failure criterion similar to those of static loading.

Energy based analysis of crack tip plastic zone of AA2024-T3 under cyclic loading

The plastic zone at a crack tip of the commercially available aluminum alloy AA2024-T3 was energetically analyzed by digital image correlation and coupled FEM simulations. In mode I, mode II and mixed mode experiments the crack tip was cyclically loaded by the same maximum equivalent stress intensity factor. In every load maximum and minimum a digital image of the crack tip area was taken to compute the displacement field using digital image correlation (DIC). The computed displacement field was mapped on the nodes of a 2d FE-model. Using a bilinear isotropic hardening model the stresses and the plastic strain energy as a measurement for the damage accumulation in the plastic zone was computed. Beyond that a postprocessor for the DIC based strain fields has been programmed to calculate the actual stress intensity factors during cyclic loading.

An investigation on crack growth rate of fatigue and induction heating thermo-mechanical fatigue (TMF) in Hastelloy X superalloy via LEFM, EPFM and integration models

In this research, fatigue and induction heating thermo-mechanical fatigue (TMF) were performed on Hastelloy X superalloy in the small and large scale yielding in plane stresses mode. The crack growth rates were measured and formulated by fracture mechanics parameters. Furthermore, the fatigue life was predicted by employing resistance curves technique. The TMF behavior of this superalloy was investigated. The results demonstrated that in-phase loading TMF conditions lead to short fatigue life (more crack growth rate) at high strain amplitudes and temperatures up to 600°C. For higher temperatures, the predominant damage was due to creep. A model based on damage contributions due to pure fatigue and cyclic creep has been presented for predicting TMF crack growth rates. Fracture mechanic method was used to suggest a model for fatigue part of TMF crack growth rate, while the temperature effects during TMF crack growth rate was considered to be due to cyclic creep. In addition the TMF crack healing or crack closure occur during application of induced eddy currents were investigated explicitly, as environmental effects of induction heating. The results show the higher current density in the crack tip area produced more heat and resulted in a significant rise in temperature. So it was concluded that the compressive thermal stress due to change of thermal expansion causes crack healing.

Experimental Determination of Crack Driving Forces for Small Cracks

The crack tip field of small fatigue cracks was measured using digital image correlation DIC. For this purpose, smooth specimen were fatigued until a certain amount of damage was visible on the surface. This specimens were then placed in a micro-tensile device in the SEM. The grey value patterns obtained at two different load levels were analyzed with DIC. Fitting the Williams series for the crack tip field to the corresponding DIC-displacement field in the crack tip area yielded the mode-I, and the mode-II stress intensity factors together with the T-stresses. It was found that the experimental values of the stress intensity factor were comparatively high with pronounced mode-II contributions.

Formation mechanism of inclined fatigue-cracks in ultrafine-grained Cu processed by equal channel angular pressing

The formation mechanism of inclined fatigue-cracks in ultrafine-grained Cu processed by equal channel angular pressing was studied by using a partially notched specimen in which a fatal natural crack was introduced, to a specific site of the smooth surface was feasible regardless of microstructural inhomogeneity caused by the processing. The crack growth direction depended on the location along the circumferential direction of the round bar specimen and on the applied stress amplitudes. The role of the microstructure and deformation mode at the crack-tip areas on the formation behavior of fatal cracks is discussed in terms of the microstructural evolution caused by cyclic stressing and the mixed-mode stress intensity factor. The in-plane shear mode deformation at the crack tip assisted the formation of the inclined crack paths and the unique crack face profile.

Growth behavior of fatigue cracks in ultrafine grained Cu smooth specimens with a small hole

In order to study the growth mechanism of fatigue cracks in ultrafine grained copper, stresscontrolled fatigue tests of round-bar specimens with a small blind hole as a crack starter were conducted. The hole was drilled on the surface where an intersection between the shear plane of the final ECAP processing and the specimen surface makes an angle of 45° or 90° with respect to the loading axis. At a low stress ( ? a = 90 MPa), the direction of crack paths was nearly perpendicular to the loading direction regardless of the location of the hole. Profile of crack face was examined, showing the aspect ratio (b/a) of b/a = 0.82. At a high stress ( ? a = 240 MPa), although the growth directions inclined 45° and 90° to the loading-axis were observed depending on the location of the drilling hole, crack faces in these cracks were extended along one set of maximum shear stress planes, corresponding to the final ECAP shear plane. The value of aspect ratios was b/a = 0.38 and 1.10 for the cracks with 45° and 90° inclined path directions, respectively. The role of deformation mode at the crack tip areas on crack growth behavior were discussed in terms of the mixed-mode stress intensity factor. The crack path formation at high stress amplitudes was affected by the in-plane shear-mode deformation at the crack tip.

The Measurement of the Fatigue Crack-Tip Displacement and Strain Fields under High Frequency Resonant Loading Applying DIC Method

In order to measure the displacement and strain field in the fatigue crack tip area of CT specimens under high frequency resonant loading condition in the fatigue crack propagation test, a method based on the digital image correlation (DIC) and digital high-speed photography technology are proposed in this paper. First, a series of digital speckle images of CT specimen under sinusoidal alternating load were collected by digital high-speed photography equipment, the displacement and strain fields within the region of crack tip in each image were calculated by DIC. The sinusoidal changing strain curve has been obtained by the least square sine wave fitting method, and the characteristic parameters of sinusoidal strain are calculated, such as the amplitude, frequency, phase, mean load . The images of characteristic position in one stress cycle were obtained by comparing the fitted sine curve of strain with the corresponding speckle images. Finally, the dynamic strain gauge was used to measure the strain at crack tip point during one stress cycle, and the accuracy and feasibility of DIC method were verified by the experimental results. The study result presented in this paper will supply a foundation for exploring the crack propagation law and measuring the fatigue crack growth parameters under high frequency resonant loading condition further.

OS1416-110 高分解能電子顕微鏡法を用いたき裂先端応力遮蔽場の直接観察

Strain field around a dislocation-pair in a silicon single crystal was visualized from images taken with a high-resolution electron microscope (HRTEM). It was quantitatively confirmed that the strain field around the dislocation pair is measured comparing with the strain field calculated from isotropic elastic theory. In order to clarify the existence of shielding effect at a crack tip due to dislocations, a strain field around a {011} crack tip with dislocations was measured using HRTEM. The crack tip area was thinned using an iron-milling machine. It was found that the strain field around the crack tip is compressive, exhibiting the existence of the shielding effect due to dislocations in atomistic scale.

Fatigue Life Prediction Based on Crack Growth Analysis Using an Equivalent Initial Flaw Size Model: Application to a Notched Geometry

Several methods for fatigue life prediction of structural components have been proposed in literature. The fatigue life prediction based on crack growth analysis has been proposed to assess the residual fatigue life of components, which requires the definition of an initial flaw. Alternatively, Fracture Mechanics crack growth-based fatigue predictions may be used to simulate the whole fatigue life of structural components assuming that there are always initial defects on materials, acting as equivalent initial cracks [1,2]. This latter approach is applied to a notched plate made of P355NL1 steel [3]. Fatigue crack growth data of the material is evaluated using CT specimens, covering several stress R-ratios. Also, S-N fatigue data is available for the double notched plate, for a stress R-ratio equal to 0 [3]. An estimate of the equivalent initial flaw size is proposed, using a back-extrapolation calculation [1,2]. The crack propagation model takes into account the elastic–plastic deformations in the crack-tip area within the calculation, based on the cyclic J-integral method. The performances of predictions are analyzed and deviations discussed.

Dynamic fracture research based on XFEM and its application on discharge valve guard of hydrogen compressor

The structural safety analysis under complex environment and load conditions is at the leading edge of engineering researches. The dynamic fracture research based on Extended Finite Element Method (XFEM) is probed into in the paper, and the modeling principle of strong discontinuities based on XFEM is applied to dynamic fracture mechanics to overcome the difficulty of defining meshes around crack tip without remeshing. XFEM-based dynamic interaction integral method is developed to reduce the calculation error caused by the non-matching meshes in the crack-tip area. Typical examples, the edge crack plate and central inclined crack plate under Heaviside function type impact loads, are taken to validate effectiveness of the method. Furthermore, as an engineering application, a valve guard subjected to impact load is simulated using the method, and numerical simulation results suggest that the valve guard is relatively safe under static load without hydrogen environment, but the real operating conditions with both hydrogen environment and dynamic load, will lead to higher brittle fracture risk for the valve guard.

In-situ SEM investigation of sub-microscale deformation fields around a crack-tip in silicon

A combination of in-situ scanning electron microscopy (SEM) and geometric phase analysis (GPA) was used to study the deformation fields around a crack-tip in single-crystal silicon under uniaxial tensile load. The sub-microscale silicon pillars grating was fabricated using holographic lithography followed by inductively coupled plasma etching. A series of SEM images of dynamic crack with the sub-microscale grating were obtained during tensile testing. The strain fields around the crack-tip were mapped by GPA. The strain fields were compared with the linear elastic fracture mechanics solutions. It was determined that the deformation is performed around the crack-tip area. The normal strain εxx and shear strain εxy are nearly zero, and the strain fields are dominated by the normal strain εyy component. With the increase of displacement load, the crack propagated mainly along the [010] crystal direction and the strains around the crack-tip increased gradually. It is noted that the theoretical prediction is lower than the experimental results from 0 to 2μm ahead of the crack-tip. However, the agreement between experimental results and theoretical prediction is very good far from the crack-tip (>2μm).

Quantitative analysis of nanoscale deformation fields of a crack-tip in single-crystal silicon

A mode II crack in single-crystal silicon was investigated experimentally using high-resolution transmission electron microscopy. Geometric phase analysis and numerical moire method were employed to map the deformation fields of the crack-tip area. The normal strain field maps of the crack-tip area indeed showed the deformation occurs primarily in the vicinity of the dislocations and the normal strains are near zero in the crack-tip area. The shear strain field map shows that the relatively large shear strain is in the crack-tip area. The experimental results were compared with the predictions of linear elastic fracture mechanics. The comparison shows that measured strain distribution ahead of the crack-tip agrees with the predictions of linear elastic fracture mechanics up to 1 nm from the crack-tip.