Effective Stress Intensity Factor Research Articles

Crack Arrest Analysis of Components With Compressive Residual Stress

ABSTRACTA finite element analysis and fracture mechanics methodology for determining the autofrettage pressure required to cause crack arrest in components under varying pressure loading are presented. Superposition of the autofrettage residual stress distribution and working load stress distribution is combined with ANSYS Separating Morphing and Adaptive Remeshing Technology (SMART) to determine the effective stress intensity factor as the crack grows. The condition for crack arrest is identified by comparison with a crack arrest model defining the crack propagation threshold stress intensity factor range for microstructurally short, physically short, and long cracks. The crack propagation threshold models of El Haddad and Chapetti are implemented and applied to fatigue analysis of stainless steel and low carbon steel double notch tensile test specimens with preinduced compressive residual stress. Based on comparison with fatigue test results, the Chapetti model is selected for use in the analysis of a 3D aluminum alloy valve body. The calculated minimum autofrettage pressure required to give crack arrest under a given working load cycle is found to be in good agreement with experimental observations from the literature.

Effective stress intensity factor range for fatigue cracks propagating in mixed mode I-II loading

The actual service axles are often subjected to mixed-mode loading, and predicting the mixed-mode I-II crack propagation behaviour using the mode I effective stress intensity factor (ΔKI) differs from the real service conditions. To effectively predict the fatigue crack propagation behaviour of actual service structures, the I-II stress intensity factor range (ΔKP-R) considering two closure effects was adopted to describe the fatigue crack propagation under mixed mode loading. A test database was established based on monitoring data of mode I and mixed-mode I-II (30/45/60°) crack propagation tests under different stress ratios. Combining domain knowledge and symbolic regression (SR) methods, an angle factor was proposed for constructing correlation functions between ΔKI and ΔKP-R. The results showed that the loading angle (α) only affects the initial projection of the load parallel and perpendicular to the fatigue crack growth (FCG) direction. Compared with the geometric correction factor, the correlation function acquired by the angle factor constructed by the SR method has higher accuracy, and the balance parameters (SCORE) obtained by the former are significantly higher than those obtained by the latter under the same function complexity. The SR verification results demonstrated that constructing mode I and I-II correlation functions with angle factors has a good predictive effect.

Crack propagation retardation behavior of shattered rim in the railway wheel

Shattered rim, known as “wheel cancer”, is a century-old problem that restricts the reliability of railway wheels. Crack propagation retardation of shattered rim in the railway wheel was investigated in this paper. First, a full-scale wheel-rail bench test rig was used to conduct wheel-rail tests on a wheelset with an interior rim crack taken from service. The interior rim crack did not propagate over the entire 50000 km distance. Cracks initiated from the two through-rim defects and propagated at a slow speed. Then, equivalent tests were conducted to investigate crack propagation behavior of the shattered rim. The crack growth rate increased with the increase of crack length for the specimen under tension–torsion loading, while that decreased with the increase of crack length for the specimens under pure-torsion and compression-tension loading. The crack propagation retardation is attributed to the compression and friction of the crack surfaces. Finally, a model was developed to describe crack propagation retardation in shattered rims. The effective stress intensity factor predicted by the model initially increases and then gradually decreases. The shattered rim has a critical size at different depths from the tread under constant amplitude load. The predicted critical size decreases with the increase of the depth.

On the Link between Plastic Wake Induced Crack Closure and the Fatigue Threshold

This purpose of this paper is to examine the relationship between crack growth equations based on Elber’s original plastic wake induced crack closure concept and the fatigue threshold as defined by the American Society for Testing and Materials (ASTM) fatigue test standard ASTM E647-15el. It is shown that, for a number of conventionally manufactured metals, the function U(R), where R is the ratio of the minimum to maximum applied remote stress, that is used to relate the stress intensity factor ΔK to the effective stress intensity factor ΔKeff is inversely proportional to the fatigue threshold ΔKth(R). This finding also results in a simple closed form equation that relates the crack opening stress intensity factor Ko(R) to ΔK, Kmax, and the fatigue threshold terms ΔKth(R) and ΔKeff,th. It is also shown that plotting da/dN as function of ΔK/ΔKth(R) would appear to have the potential to help to identify the key fracture mechanics parameters that characterise the effect of test temperature on crack growth. As such, for conventionally manufactured metals, plotting da/dN as function of ΔK/ΔKth(R) would appear to be a useful addition to the tools available to assess the fracture mechanics parameters affecting crack growth.

Fatigue Crack Growth Rates and Crack Tip Opening Loads in CT Specimens Made of SDSS and Manufactured Using WAAM.

Additive manufacturing offers greater flexibility in the design and fabrication of structural components with complex shapes. However, the use of additively manufactured parts for load-bearing structural applications, specifically involving cyclic loading, requires a thorough investigation of material fatigue properties. These properties can be affected by many factors, including residual stresses and crack tip shielding mechanisms, which can be very different from those of conventionally manufactured materials. This research focuses on super duplex stainless steels (SDSSs) fabricated with wire arc additive manufacturing (WAAM) and investigates their fatigue crack growth rates and the net effect of crack tip shielding mechanisms. Using the compliance-based method, we measured crack tip opening loads in compact tension (CT) specimens with cracks propagating longitudinally and transversely to the WAAM deposition direction. It was found that fatigue crack growth rates were very similar in both directions when correlated by the effective stress intensity factor range. However, the differences in crack tip opening loads explain a quite significant influence of the deposition direction on the fatigue life.

Cutting-edge insights: Crack growth rates in 9% Ni steel from room to cryogenic conditions influenced by crack closure and effective stress intensity factors

This study investigates the fatigue crack growth rate of 9% Ni steel at varying stress ratios under both room and cryogenic temperatures, attributing different growth rates to the phenomenon of crack closure. Traditional methods of studying crack closure, including the opening force, compliance ratio, and adjusted compliance ratio techniques, are assessed. Our results are juxtaposed with previous formulae for the opening force technique, leading to the introduction of a new formula that incorporates temperature effects by normalising the stress intensity factor with the yield strength at the respective test temperature. We highlight the adjusted compliance ratio (ACR) technique's limitations at cryogenic temperatures due to challenges in measuring notch open-crack compliance. As a solution, we present an innovative method that determines compliance using the effective elastic modulus. The mechanics behind the ACR technique are elucidated through the lens of the wedging mechanism. Our insights reveal that the ACR technique precisely calculates the effective stress intensity factor range (ΔKeff) under specific conditions. We address existing limitations by introducing a novel method, the triple compliance ratio (TCR) technique. A comparative analysis of effective stress intensity factors from all four techniques reveals the TCR technique's superior ability to correlate crack closure with crack growth. By eliminating the crack closure effect, the TCR technique offers a more accurate prediction of fatigue crack growth rate across diverse load ratios.

Experimental Data-Driven approach for the evaluation of crack tip opening loads under variable amplitude loading

In this paper, we present a new data-driven approach for the evaluation of crack tip opening load (Pop) values under variable amplitude loading. These values are analysed for CT specimens manufactured from common aircraft grade aluminium alloys and subjected to several load sequences, all of which have a relatively high R-ratio content without significant overloads and underloads. Direct experimental measurements and outcomes of numerical simulations indicate that the Pop change abruptly from cycle to cycle. For this type of fatigue loading (including a military transport aircraft load spectrum with more than 400,000 turning points) and materials, it was found that Pop is well described by a linear function of the preceding minimum and maximum values of the applied loading. This finding provides a new simple way to evaluate the effective stress intensity factor range, which is often considered as a fatigue crack driving force. It is also verified via the use of machine learning that the proposed approach is capable of predicting the mean stress (R-ratio) effect on Pop for block loading. Therefore, the developed data-driven approach is a promising alternative to the computational methods, which currently dominate advanced fatigue life assessment procedures.

The Two-Parameter Fracture Criterion Taking into Account Two-Dimensional Deformation Constraints at the Front of a Mixed-Type Crack

In this article, a new fracture criterion for a mixed-type crack (type I + type II) is proposed. It is based on the assumption that the maximum tangential stresses in the prefracture region are equal to the local strength of the material. In this case, the size of the prefracture area and the local strength are determined taking into account nonsingular Тхx and Тzz stresses included in the expansion of the Williams stress function. The use of Тхx and Тzz stresses in the calculations allows one to describe the two-dimensional local constraint of the deformation along the crack front in three-dimensional bodies. In addition to KI and KII, the expression for the effective stress intensity factor (SIF) includes the ratios of the Тхx and Тzz stresses to the yield strength. This makes it possible to take into account the constraint of deformations in the transverse and longitudinal directions of the crack front, respectively. An example of the implementation of the developed criterion in relation to the determination of the fracture load of a tensile-stressed plate with a through inclined crack is given. Dependences of the Тxx and Тzz stresses on the plate thickness are presented for various crack slopes and plate thicknesses. It is shown that an increase in the plate thickness and a decrease in the crack slope lead to a decrease in the fracture load.

Presentation of machine learning methods and multi-objective optimization of fracture indices for asphalt rubber mixtures containing wax-based warm mix additives modified by nano calcium carbonate

Warm mix asphalt (WMA) additives have been proposed to overcome the high viscosity problem of crumb rubber modified asphalt (CRMA) binders. Various additives have been used to improve the low-temperature cracking performance of asphalt mixtures, but no study has been conducted to present the optimum additive content in CRMA binders in different loading modes. Therefore, this research aims to present the optimum content of nano calcium carbonate (NCC) to improve the fracture toughness and energy of asphalt rubber mixtures containing WMA additives (slack wax (SW) and polypropylene wax (PPW)). The semi-circular bend (SCB) fracture test was applied under pure mode I, mixed mode I-II, mixed mode II-I and pure mode II loadings at subzero temperature. Machine learning methods, including multivariate regression (MVR) and artificial neural network (ANN) models of group method of data handling (GMDH) and multilayer perceptron (MLP), were used to provide the prediction models of effective stress intensity factor (Keff) and fracture energy (Gf). Finally, the multi-objective optimization of Keff and Gf was performed to obtain optimum NCC content. The results indicated that in MVR model, the outputs had a small correlation with laboratory values, so that R value of MVR was 0.8406 and 0.8011 for Keff and Gf, respectively. Also, it was revealed in MVR that NCC had the highest impact on Keff and Gf significantly. GMDH model results showed that the relationships between predicted and laboratory values of Keff and Gf are appropriately described with R value of 0.9546 and 0.9229 for Keff and Gf models, respectively. In MLP model, different layer structures of the feed-forward neural network were developed to obtain the most accurate structure. It was indicated that MLP with 4–22–1 and 3–19–1 structures had a higher accuracy for Keff and Gf prediction models with R value of 0.9951 and 0.9978, respectively. Finally, by the use of the best model relationships, the results of the multi-objective optimization indicated that 4.91% and 6.37% NCC were the design optimum contents resulting in a maximum of Keff and Gf simultaneously for SW and PPW-modified CRMA mixtures. Moreover, the optimum NCC contents in loading modes of mode mixity Me of 1, 0.8, 0.4 and 0 were 3.62%, 5.12%, 4.08% and 3.42% for SW-modified CRMA mixtures and 4.35%, 6.51%, 7.19% and 2.84% for PPW-modified CRMA mixtures, respectively.

The Two-Parameter Fracture Criterion Taking into Account Two-Dimensional Deformation Constraints at the Front of a Mixed-Type Crack

In this article, a new fracture criterion for a mixed-type crack (type I + type II) is proposed. It is based on the assumption that the maximum tangential stresses in the prefracture region are equal to the local strength of the material. In this case, the size of the prefracture area and the local strength are determined taking into account nonsingular Тхx and Тzz stresses included in the expansion of the Williams stress function. The use of Тхx and Тzz stresses in the calculations allows one to describe the two-dimensional local constraint of the deformation along the crack front in three-dimensional bodies. In addition to KI and KII, the expression for the effective stress intensity factor (SIF) includes the ratios of the Тхx and Тzz stresses to the yield strength. This makes it possible to take into account the constraint of deformations in the transverse and longitudinal directions of the crack front, respectively. An example of the implementation of the developed criterion in relation to the determination of the fracture load of a tensile-stressed plate with a through inclined crack is given. Dependences of the Тxx and Тzz stresses on the plate thickness are presented for various crack slopes and plate thicknesses. It is shown that an increase in the plate thickness and a decrease in the crack slope lead to a decrease in the fracture load.

Fatigue crack propagation behavior in Ti−6Al−4V alloy with surface gradient structure fabricated by high-energy shot peening

A gradient structure was successfully fabricated on the surface of Ti−6Al−4V alloy by high-energy shot peening (HESP), and its effect on fatigue crack propagation was investigated. Optical microscope, scanning electron microscope, transmission electron microscope and X-ray diffractometer were used to characterize the microstructure and residual stress evolution during HESP. The results show that a gradient nanostructure with residual compressive stress layer of 220 μm in depth is formed. The generation of gradient nanostructures improves the strength−ductility combination of the alloy. Maximum residual compressive stress is generated on the subsurface, which gradually increases with the increase of shot peening time. HESP treatment effectively reduces the crack propagation rate and increases the fatigue crack propagation life. The residual compressive stress reduces the effective stress intensity factor range at crack tip, thereby generating the crack closure effect and delaying the crack propagation. At the same time, the synergy effects of increase in grain boundaries, decrease in effective slip length and the plastic zone at the crack tip caused by the refinement of the surface grains can increase the crack propagation resistance as well.

Prediction of the durability of a plate with a through crack taking into account biaxial constraints of deformations along the front of a normal rupture crack

A methodology for evaluating the durability of plate elements of structures taking into account biaxial constraints of deformations along the front of a normal rupture crack (Mode I crack) is presented. The absence of the available literature data in which the prediction of the crack growth is carried out using Txx- and Tzz-stresses which are non-singular terms in the Williams expansion for stresses at the crack tip is noted. The calculation of the fatigue crack growth rate is based on the Paris equation in which the range of the effective SIF is used instead of the range of the usual stress intensity factor (SIF). In this case, the expression for the effective SIF includes Txx- and Tzz-stresses in addition to the usual SIF. This approach provides taking into account, for example, the thickness of the plate for predicting the durability, which is impossible when only the SIF and Txx-stresses are used. The formula for the effective SIF is derived proceeding from the assumption that tangential stresses in the pre-fracture zone are equal to the local strength of the material. In this case, the size of the pre-fracture zone and the local strength of the material are determined taking into account Txx- and Tzz-stresses. The numerical simulation is based on the proprietary finite-element program which allows calculating Txx- and Tzz-stresses at the front of a through crack in a plate subjected to cyclic uniaxial and biaxial tension. It is shown that nonsingular Txx-stresses primarily describe the effect of biaxial loading on the survivability, whereas Tzz-stresses describe the effect of the plate thickness on the survivability. It is shown that with increasing thic kness of the plate the value of the effective SIF increases due to the increased constraint along the crack front, thus increasing the crack growth rate and decreasing the survivability. With an increase in the stress ratio R, under the condition of a constant stress range, the maximum effective SIF reaches the critical value equal to the fracture toughness much faster thus reducing the durability. It is shown that for uniaxial cyclic tension, the durability predicted by the proposed methodology is higher than that in the classical approach, when the conventional SIF is used in the Paris equation. For biaxial cyclic tension of a plate, an increase in stresses directed parallel to the crack banks leads to an increase of crack front constraints and therefore to a decrease in the durability compared to the classical approach. In other words, the classical theory does not always provide a conservative estimate of the durability, which indicates the expediency of using the developed method for calculating the durability taking into account biaxial constraints of deformations along the crack front.

Enhanced strength-ductility synergy of laser additive manufactured stainless steel/Ni-based superalloy dissimilar materials characterized by bionic mechanical interlocking structures

The unique mechanism of toughness enhancement found in natural materials has served as inspiration for the development of a new generation of dissimilar metal materials (DMMs). Here we present a bionic mechanical interlocking structure strategy that stainless steel 316L and Inconel 625 DMMs with an enhanced strength-conductivity trade-off processed by laser additive manufacturing (AM), possessing an ultimate tensile strength of 675.64 MPa, and a uniform elongation of 33.6%. The incompatible deformation between SS316L (plastic deformation) and IN625 (non-deformation) contributes to overcoming the strength-ductility trade-off. The integration of alternating soft and hard non-uniform structures plays a pivotal role in effectively absorbing and dissipating the energy introduced by external loads during crack propagation. This geometric arrangement and multilevel structure at the interface notably reduces the effective stress intensity factor along the crack path, leading to added resistance against loading. The multi-strengthening mechanism coupled with the heterogeneous deformability gives the material excellent strength-ductility synergy, especially the bionic mechanical interlocking structure extending the crack expansion path, which helps to avoid premature failure of weak interface layers. These findings will provide new insights into the controlled design of high-performance DMMs, which highlights the potential to inherit merits from constitutive materials for better strength-ductility combinations.

Study of Effective Stress Intensity Factor through the CJP Model Using Full-Field Experimental Data.

In this work, the Christopher-James-Patterson crack tip field model is used to infer and assess the effective stress intensity factor ranges measured from thermoelastic and digital image correlation data. The effective stress intensity factor range obtained via the Christopher-James-Patterson model, which provides an effective rationalization of fatigue crack growth rates, is separated into two components representing the elastic and retardation components to assess shielding phenomena on growing fatigue cracks. For this analysis, fatigue crack growth tests were performed on Compact-Tension specimens manufactured in pure grade 2 titanium for different stress ratio levels, and digital image correlation and thermoelastic measurements were made for different crack lengths. A good agreement (~2% average deviation) was found between the results obtained via thermoelastic stress analysis and digital image correlation indicating the validity of the Christopher-James-Patterson model to investigate phenomena in fracture mechanics where plasticity plays an important role. The results show the importance of considering crack-shielding effects using the Christopher-James-Patterson model beyond considering an exclusive crack closure influence.

A Fracture Criterion with Biaxial Constraints of Deformations along the Front of a Normal Rupture Crack

In this article, a new fracture criterion is formulated for a normal rupture crack, the most common in practice, based on the assumption that the tangential stresses in the prefracture zone are equal to the local strength of the material. In this case, the size of the prefracture area and the local strength are determined taking into account the nonsingular Тхx and Тzz stresses included in the asymptotic stress distribution according to Williams and characterizing the two-dimensional local constraint of deformation along the crack front in three-dimensional bodies. An expression for the effective stress intensity factor is obtained. In addition to the classical stress intensity factor, it includes the ratios of the Тxx and Тzz stresses to the yield strength. This makes it possible to take into account the restriction of deformations in the transverse (due to Тxx stresses) and longitudinal (due to Тzz stresses) directions in the vicinity of the crack front. Verification of the developed software tools and the proposed fracture criterion has been carried out. Examples of the implementation of the developed criterion for assessing crack resistance of a plate stretched in one or two directions with a coaxial transverse crack are given.

The Improved Irwin’s Model for Crack Problems in Power-Law Hardening Materials

In this paper, an improved Irwin’s model for power-law hardening materials is established through the static equivalence between the linear elastic stress solution and the stress redistribution in the plasticity-affected zone (PAZ) under small-scale yielding (SSY) conditions. HRR solution is adopted to describe the stress field within the crack-tip plastic zone (CTPZ). Analytical expressions of the effective stress intensity factor (SIF) and the size of PAZ are derived to illustrate the effect of CTPZ on the fracture behavior for power-law hardening materials. Influences of external load and hardening exponent on fracture behavior are explored. The proposed model can assess the toughening effect of CTPZ accurately using the SIF ratio, which is always smaller than 1. This model can be applied to various materials obeying power-law hardening constitutive equations. It will reduce to the extended Irwin’s model for elastic-perfectly plastic materials in the limiting case.

Mixed mode crack growth behaviour considering plasticity-induced and roughness-induced closure

A theoretical analytical solution of the Christopher-James-Patterson (CJP) model in mixed mode is presented in this paper, where the influence of roughness-induced crack closure (RICC) on fatigue crack growth is considered and a new effective stress intensity factor range (ΔKP-R) is proposed as the driving force for crack propagation. The solution showed that both the maximum tangential stress criterion (MTS) and the minimum strain energy density criterion (S) can reasonably well predict the crack deflection angle. Experimental testing on EA4T axle steel samples showed that both the 8 % compliance offset criterion in the conventional ASTM procedure and the parabolic-line method were suitable for the determination of the crack-opening force. The solution includes plasticity-induced crack closure (PICC) and RICC effects, therefore the crack propagation behaviour can be described in a more effective way. Compared with the traditional mixed model crack growth models with higher fitting correlation coefficient, the fitting effect of the CJP model has been improved by 12 % in this solution, and the residual stress in the pre-crack stage increased the crack-closure level. Due to the influence of residual stress, the rate of roughness value (RA) showed a fluctuation of 4.5 %, which indirectly affected the fatigue crack growth rate (FCGR) of the test.

Integrating SMA and CFRP for fatigue strengthening of edge-cracked steel plates

Inclined fatigue cracks of U-ribs and diaphragms in orthotropic steel-box girders are challenging to be repaired using prestressing techniques. Integrating shape memory alloys (SMAs) and carbon fibre reinforced polymers (CFRPs) can achieve a hybrid self-prestressing strengthening approach for such fatigue cracks. To examine the strengthening effect of this approach on inclined cracks, 39 specimens were prepared in four groups and tested under static and fatigue tensioning in this study. Both static and fatigue test results showed that SMA/CFRP composite strengthening effectively retard steel cracking. Compared to control specimens, SMA/CFRP composite strengthening enhanced the notch tip yield load by 128% and 111% for specimens with a notch inclination of 0° and 30°, and the corresponding fatigue life by 7.62 and 8.69 times, respectively. Besides, the strengthening effect of combining SMA and CFRP (SMA/CFRP composite) on cracked steel plates was greater than that of either SMA or CFRP alone, particularly for the steel plates with an inclined crack. Finally, the calculation of mixed-mode I/II effective stress intensity factors confirmed the superior strengthening effect of SMA/CFRP composite on steel plates with an inclined crack. The findings of this study can provide a reference for the reinforcement of orthotropic steel-box girders.

A modified formula for cyclic compression crack growth model considering compressive load effect

Fatigue crack growth under cyclic compression has been confirmed by experiments and widely exists in engineering applications, with the expression of stress intensity factor often serving as milestones. A typical difficulty in calculating the stress intensity factor under cyclic compression is the effect of compressive load on fatigue crack growth. Compressive load effect, resulting in the change of plastic zone and residual stress near crack tip, is a long-term challenge for predicting fatigue crack growth life. We modify the expression of effective stress intensity factor to predict fatigue crack growth life based on the distribution of residual stress, and analyze the effect of load characteristics. It considers the characteristic of material and load, and calculates the driving force of crack growth by integrating the residual stress in plastic zone. In the study of fatigue crack growth experiments under cyclic compression, the modified formula is proved to improve, by comparative analysis, the predictive ability on the whole range of experiment data. Consequently, the modified formula is conducive to calculate the fatigue crack growth.

Mixed-mode fracture model to quantify local toughness in nacre-like alumina

With the progress of ceramic engineering, tough technical ceramics such as nacre-like alumina now exhibit complex fracture patterns with high degrees of deflection, branching and bridging. If these mechanisms highly contribute to improving crack resistance, the crack geometries go beyond the hypotheses assumed in standard techniques to quantify toughness, making it difficult to understand the mechanisms responsible for crack propagation. We report a robust local solution based on a combination of analytical formulas and finite element analysis to accurately estimate the effective stress intensity factors at the tips of multiple deflected cracks. The influence of sample size on local R-curves is analysed and shown to be less important relative to standard methods. We use this method to evaluate the direct influence of zirconia nanoparticles in the nacre-like structure and highlight the role of these findings in the understanding of mechanical response and future optimisation of highly textured tough ceramics.