Unified characterisation of in‐plane and out‐of‐plane constraint based on crack‐tip equivalent plastic strain

Constraint can be divided into two conditions of in‐plane and out‐of‐plane, and each of them has its own parameter to characterize. However, in most cases, there exists a compound change of both in‐plane and out‐of‐plane constraint in structures, a unified measure that can reflect both of them is needed. In this paper, the finite element method (FEM) was used to calculate the equivalent plastic strain (ɛ_p) distribution ahead of crack tips for specimens with different in‐plane and out‐of‐plane constraints, and the FEM simulations based on Gurson–Tvergaard–Needleman (GTN) damage model and a small number of tests were used to obtain fracture toughness for the specimens with different constraints. Unified measure and characterisation parameter of in‐plane and out‐of‐plane constraints based on crack‐tip equivalent plastic strain has been investigated. The results show that the area A_PEEQ surrounded by the ɛ_p isoline ahead of crack tips can characterize both in‐plane and out‐of‐plane constraints. Based on the area A_PEEQ, a unified constraint characterisation parameter A_p was defined. It was found that there exists a sole linear relation between the normalised fracture toughness J_IC/J_ref and regardless of the in‐plane constraint, out‐of‐plane constraint and the selection of the ɛ_p isolines. The unified J_IC/J_ref−reference line can be used to determine constraint‐dependent fracture toughness of materials. The FEM simulations with the GTN damage model (local approach) can be used in obtaining the unified J_IC/J_ref−reference line for materials with ductile fracture.     

Three‐dimensional analyses of in‐plane and out‐of‐plane crack‐tip constraint characterization for fracture specimens

Three‐dimensional elastic–plastic finite element analyses have been conducted for 21 experimental specimens with different in‐plane and out‐of‐plane constraints in the literature. The distributions of five constraint parameters (namely T‐stress, Q, h, T_z and A_p) along crack fronts (specimen thickness) for the specimens were calculated. The capability and applicability of the parameters for characterizing in‐plane and out‐of‐plane crack‐tip constraints and establishing unified correlation with fracture toughness of a steel were investigated. The results show that the four constraint parameters (T‐stress, Q, h and T_z) based on crack‐tip stress fields are only sensitive to in‐plane or out‐of‐plane constraints. Therefore, the monotonic unified correlation curves with fracture toughness (toughness loci) cannot obtained by using them. The parameter A_p based on crack‐tip equivalent plastic strain is sensitive to both in‐plane and out‐of‐plane constraints, and may effectively characterize both of them. The monotonic unified correlation curves with fracture toughness can be obtained by using A_p. In structural integrity assessments, the correlation curves may be used in the failure assessment diagram (FAD) methodology for incorporating both in‐plane and out‐of‐plane constraint effects in structures for improving accuracy.     

Strain rate concentration and dynamic stress concentration for double‐edge‐notched specimens subjected to high‐speed tensile loads

Engineering plastics provide superior performance to ordinary plastics for wide range of the use. For polymer materials, dynamic stress and strain rate may be major factors to be considered when the strength is evaluated. Recently, high‐speed tensile test is being recognized as a standard testing method to confirm the strength under dynamic loads. In this study, therefore, high‐speed tensile test is analysed by the finite element method; then, the maximum dynamic stress and strain rate are discussed with varying the tensile speed and maximum forced displacement. The maximum strain rate increases with increasing the tensile speed u/t, but the strain rate concentration factor is found to be constant independent of tensile speed, which is defined as the maximum strain rate appearing at the notch root over the average nominal strain rate at the minimum section . It is found that the strain rate at the notch root depends on the dynamic stress rate at the notch root and independent of the notch root radius ρ. It is found that the difference between the static and dynamic maximum stress concentration (σ_yA,max ? σ_yA,st) at the notch root is proportional to the tensile speed when u/t = 5000 mm/s. Strain rate concentration factors are also discussed with varying the notch depth and specimen length. Based on the elastic strain rate concentration factor, the master curve is obtained useful for understanding the impact fracture of polycarbonate for the wide range of temperature and impact speed.     

Short and long crack data for fatigue of 2024‐T3 Al sheets: binariness of scale segmentation in space and time

Pedagogically speaking, crack initiation–growth–termination (IGT) belongs to the process of fracture, the modelling of which entails multiscaling in space and time. This applies to loadings that are increased monotonically or repeated cyclically. Short and long crack data are required to describe IGT for scale ranges from nano to macro, segmented by the SI system of measurement. Unless the data at the nano scale can be connected with the macro, IGT remains disintegrated. The diversity of non‐homogeneity of the physical properties at the different scale ranges results in non‐equilibrium. These effects dubbed as non‐equilibrium and non‐homogeneous are hidden in the test specimens and must be realized. They can be locked into the reference state of measurement at the mi‐ma scale range by application of the transitional functions and transferred to the nano‐micro and macro‐large scale ranges. The aim of this work is to convert the ordinary crack length data to those referred to as short cracks that are not directly measurable. All test data are material, loading and geometry (MLG) specific. The results obtained for the 2024‐T3 aluminium sheets hold only for the MLG tested. The differences are more pronounced for the short cracks. These effects can be revealed by comparing the incremental crack driving force (CDF) for the ma‐mi range the ma‐large range and the na‐mi range The CDF is equivalent to the incremental volume energy density factor (VEDF). The incremental mi‐ma CDF is found to be 10–10⁵ kg mm^?1 for cracks 3–55 mm long travelling at an average velocity of 10^?5 mm s^?1. The crack velocity rises to 10^?3 mm s^?1 when the incremental CDF is increased to 10⁵–10⁶ kg mm^?1, while the crack lengths are 49–260 mm. The crack velocity for the na‐mi range of 0.040–0.043 mm slowed down to 10^?8 mm s^?1, and the incremental CDF reduces further to 10^?8–10^?2 kg mm^?1. Note that changed several orders of magnitude while the crack advanced from 0.040 to 0.044 mm. Such behaviour is indicative of the highly unstable nature of nanocracks. All results are based on using the transitionalized crack length (TCL). The TCL fatigue crack growth increment Δa is postulated to depend on the incremental CDF ΔS or ΔVEDF. The form invariance of , and is invoked by scale segmentation to reveal the multiscale nature of IGT that is inherent to fatigue crack growth. While the choice of directionality from micro to macro is not the same as that from macro to micro, this difference will not be addressed in this work.     

Three‐dimensional analyses of unified characterization parameter of in‐plane and out‐of‐plane creep constraint

Based on extensive three‐dimensional finite element analyses, the unified characterization parameter A_c of in‐plane and out‐of‐plane creep constraint based on crack‐tip equivalent creep strain for three specimen geometries (C(T), SEN(T) and M(T)) were quantified for 316H steel at 550 °C and steady‐state creep. The distributions of the parameter A_c along crack fronts (specimen thickness) were calculated, and its capability and applicability for characterizing a wide range of in‐plane and out‐of‐plane creep constraints in different specimen geometries have been comparatively analysed with the constraint parameters based on crack‐tip stress fields (namely R*, h and T_Z). The results show that the parameter A_c in the centre region of all specimens appears uniform distribution and lower value (higher constraint), and in the region near free surface it shows protuberant distribution and higher value (lower constraint). The parameter A_c can simultaneously and effectively characterize a wide range of in‐plane and out‐of‐plane creep constraints, while the parameters R*, h and T_Z based on crack‐tip stress fields cannot achieve this. The different capabilities of these parameters for characterizing in‐plane and out‐of‐plane creep constraints originate from their underlying theories. The parameter A_c may be useful for accurately characterizing the overall constraint level composed of in‐plane and out‐of‐plane constraints in actual high‐temperature components, and it may be used in creep life assessments for improving accuracy.     

An investigation on the effects of equal channel angular pressing on the mixed‐mode fracture toughness and mechanical properties of 6063 aluminium alloy

In this study, effects of equal channel angular pressing (ECAP) on the mixed‐mode fracture toughness of Al‐6063 were investigated. The ECAP process continued up to 5 passes without failure. Grain refinement was obvious after 5 passes of the ECAP process. The average grain size reduced from 45μm to less than 1μm, and textural studies shows aligning the grains in known directions. After 4 passes, yield and ultimate strengths increase respectively from 100 and 209 MPa to 300 and 375 MPa and reduction in elongation was also observed. The microhardness improved after the process. The fracture toughness for different orientations was measured. For pure mode I (opening mode), its value decreased after the first pass from 18.4 to 15.71  ; however, it increased to about 18.8  after the fifth pass. For mixed‐mode loading condition, different orientations were investigated. The results revealed different fracture toughness reductions after the first passes of the process for specimens with different orientations. The fracture surfaces were studied by using scanning electron microscope, and refined equiaxed dimples were observed after the ECAP process.     

Study of the influence of notch radii and temperature on the probability of failure: A methodology to perform a combined assessment

The fracture assessment of notched components based on cracked components approaches leads to over‐conservative failure predictions. In the research literature, several approaches are proposed to overcome this problem using an apparent fracture toughness, . Nevertheless, most of these approaches are based on deterministic assumptions despite the large and variable scatter exhibited by for different notch radii (ρ) or temperatures (T). This paper proposes a methodology for deriving a probabilistic field including the effect of temperature on the failure of notched components. First, the theory of critical distances is applied to transform each apparent fracture toughness into the equivalent fracture toughness for ρ = 0. Then, the temperature is supposed to act as a scale effect in the Weibull cumulative distribution function of the equivalent fracture toughness, and the corresponding scale effect function is derived. Finally, the applicability of the proposed methodology is illustrated by an example using two ferritic‐pearlitic steels: S275JR and S355J2.     

Ratcheting of 304 Stainless Steel Alloys subjected to Stress‐Controlled and mixed Stress‐ and Strain‐Controlled Conditions evaluated by Kinematic Hardening Rules

The present study predicts ratcheting response of SS304 tubular stainless steel samples using kinematic hardening rules of Ohno–Wang (O–W), Chen‐Jiao‐Kim (C–J–K) and a newly modified hardening rule under various stress‐controlled, and combined stress‐ and strain‐controlled histories. The O–W hardening rule was developed based on the critical state of dynamic recovery of backstress. The C–J–K hardening rule further developed the O–W rule to include the effect of non‐proportionality in ratcheting assessment of materials. The modified rule involved terms , and in the dynamic recovery of the Ahmadzadeh–Varvani (A–V) model to respectively track different directions under multiaxial loading, account for non‐proportionality and prevent plastic shakedown of ratcheting data over multiaxial stress cycles. The O–W model persistently overestimated ratcheting strain over the multiaxial loading paths. The C–J–K model further lowered this overprediction and improved the predicted ratcheting curves. The predicted ratcheting curves based on the modified model closely agreed with experimental data under various loading paths.     

In‐plane and out‐of‐plane constraint for single edge notched bending specimen and cruciform specimen under uniaxial and biaxial loading

Considering fracture constraint is an efficient way to describe stress–strain field and fracture toughness more accurately, so it is necessary to realise the relationship with in‐plane and out‐of‐plane constraint for different standard specimens. In this paper, three‐dimensional finite element method is applied to study the in‐plane and out‐of‐plane constraint for both cruciform specimen and single edge notched bending specimen made from commercial pure titanium. Crack length and in‐plane loading as the factors affecting in‐plane constraint, and thickness as the factor affecting the out‐of‐plane constraint are used to study the effect on both in‐plane and out‐of‐plane constraint in this paper. From the results, in‐plane and out‐of‐plane constraint are both related to specimen geometries and loading styles. And there exist relationships with in‐plane and out‐of‐plane constraint because of factors for different specimens. Depending on crack length, out‐of‐plane constraint increases with in‐plane constraint. While depending on transverse loading, out‐of‐plane constraint decreases with in‐plane constraint. In addition, when the in‐plane constraint of a specimen is higher, in‐plane constraint increases with out‐of‐plane constraint (thickness). When the in‐plane constraint is lower, in‐plane constraint almost remains unchanged with out‐of‐plane constraint.     

Probabilistic model for length effect on fatigue life of longitudinal elements

This paper studies the length effect on fatigue life of longitudinal element at the macroscale. An asymptotic weakest‐link Weibull phenomenological model that incorporates a statistical length effect for the fatigue life of longitudinal element is proposed in this research. In the proposed model, the weakest‐link effect gradually becomes dominant and causes a decrease in fatigue life that increases along , the normalized length of the longitudinal element. To this end, the fatigue life under a specified stress range is divided into 3 zones according to the normalized length : (1) is the zone where length effects can be ignored, and the fatigue life can be treated as a random variable; (2) is the zone where the fatigue life is length dependent; and (3) is the zone where the fatigue life follows asymptotic length dependence. The asymptotic threshold normalized length, , can be evaluated by the asymptotic weakest‐link Weibull model. To validate the proposed model, 3 previously published datasets are used: (1) the fatigue data of Picciotto yarn, (2) hipo‐eutectoid steel wire with different lengths, and (3) the fatigue data of high‐strength steel wire with different lengths and different constant stress ranges. Finally, the results obtained by the proposed model are compared with those from the literature and discussed in detail. The analytical solutions obtained using the proposed model allows for assessment of the fatigue life of certain components and structures that are beyond current testing capabilities. In particular, the length effects on the fatigue life of the high‐strength steel wire in stay cables are investigated to gain insight into issues regarding safe designs.     

In‐plane and out‐of‐plane constraint parameters along a three‐dimensional crack‐front stress field under creep loading

Full‐field three‐dimensional (3D) numerical analyses was performed to determine in‐plane and out‐of‐plane constraint effect on crack‐front stress fields under creep conditions of finite thickness boundary layer models and different specimen geometries. Several parameters are used to characterize constraint effects including the non‐singular T‐stresses, the local triaxiality parameter, the T_z ‐factor of the stress‐state in a 3D cracked body and the second‐order‐term amplitude factor. The constraint parameters are determined for centre‐cracked plate, three‐point bend specimen and compact tension specimen. Discrepancies in constraint parameter distribution on the line of crack extension and along crack front depending on the thickness of the specimens have been observed under different loading conditions of creeping power law hardening material for various configurations of specimens.     

Toughness enhancement and equivalent initial fracture toughness of cementitious composite reinforced with aligned steel fibres

Based on theoretical analysis and numerical simulation, the impact of steel fibres on the stress intensity factor (SIF) at the crack tip for cementitious composite was studied. The enhanced toughness of steel fibre reinforced cementitious composite (SFRC) in resisting cracks was explained by the decrement of SIF caused by steel fibre inclusions at the crack tip of the composite. The equivalent initial fracture toughness was used to characterize the crack initiation of SFRC. A simplified method for determining the of SFRC was proposed based on a linear regression method. Fracture tests were conducted on three‐point bending notched beams with different steel fibre volume fractions and specimen sizes to study the crack initiation behaviour of aligned steel fibre reinforced cementitious composite (ASFRC). of ASFRC was calculated, and the size effect of was analysed. The results showed that slightly increased with the steel fibre volume fraction and gradually became stable. For the tested specimens, whose heights varied between 40 and 100 mm, the specimen size had little impact on the .     

Some remarks on the Neuber rule applied to a control volume surrounding sharp and blunt notch tips

The paper deals with the small scale yielding estimation of nonlinear stresses and strains at the root of sharp and blunt notches through the mechanical model of antiplane shear loadings. The frame stems from the relation existing between the elastic and plastic averaged strain energy densities evaluated over the control volume drawn by the energy contour lines ahead of the notch tip. The analysis proves that there exist different relationships in terms of point‐wise elastic and plastic stresses and strains at the notch tip depending whether the notch is sharp (small notch tip radius) or blunt. For sharp notches, the analysis confirms previous results obtained by the present authors, according to which . This equation accounts for the influence of the material law through the hardening exponent n. Differently, when the notch can be regarded as blunt, calculations over the control volume give , in agreement with the Neuber rule.     

S‐N curves in the very‐high‐cycle fatigue regime: statistical modeling based on the hydrogen embrittlement consideration

The continuous increment of durability and reliability requirements for many machinery components is significantly enhancing the research activity in the Very‐High‐Cycle Fatigue (VHCF) characterization of metallic materials, in particular of high‐strength steels for critical structural applications. According to the model, the VHCF strength of high‐strength steels can be estimated from the projected area of the ‘Optically Dark Area’ (ODA), which plays a key role in the VHCF response of high‐strength steels: more than 95% of the total VHCF life is consumed in the ODA formation, with crack growing even though the Stress Intensity Factor (SIF) is below the threshold for crack growth. Following the hydrogen embrittlement theory proposed by Murakami, hydrogen is supposed to assist crack growth within the ODA. The present paper proposes a general SIF formulation for the analytical model of the hydrogen assisted crack growth within the ODA. Starting from the general SIF formulation, a general expression for the material fatigue limit is obtained in the paper. The statistical method for the estimation of the parameters involved in the proposed model is finally illustrated in the paper and numerically applied to an experimental dataset.     

Anisotropic mechanical and fatigue behaviour of Inconel718 produced by SLM in LCF and high‐temperature conditions

Additive manufacturing (AM) is one of the processes with the most potential for producing components used in internal combustion engines and features high efficiency due to the possibility of building very complex shapes. Several drawbacks of parts produced using AM are still unresolved, like poor surface quality, the presence of internal defects and anisotropic mechanical behaviour, which all contribute to decreasing the fatigue strength compared with the material produced using conventional processes. The effect of building direction on both the macroscopic mechanical behaviour and the crack propagation mechanism of Ni‐base superalloy Inconel718 produced using AM was investigated under the combined effect of low cycle fatigue (LCF) and high temperature. The different crack growth mechanisms investigated using compact tension (CT) specimens, tested at high temperature, showed a significant difference between the two building directions. The LCF fatigue experiments also showed a significant difference in the ε‐N curves from the two directions together with a high level of scatter due to the dispersion of the defect size at the fracture origin. The dimensions of the defects (as measured using the parameter) were analysed by means of extreme value statistics and showed a significant difference between the two orientations investigated. The aim of this work is to propose a simplified approach (based on ΔJ_eff concepts) to estimate the fatigue life of a component produced using AM that takes into account the material variability due to the combined effect of mechanical anisotropic behaviour and the presence of defects at high‐temperature conditions.     

Crack evolution law and failure mode of red sandstone under fatigue–creep interaction

To explore the fracture characteristics of rock under the interaction of fatigue load and creep load, fatigue–creep interactive loading experiments were performed on red sandstone with prefabricated cracks. The crack evolution process and failure mode were analyzed using acoustic emission technology and digital image correlation. The results showed that crack growth mainly occurred in the fatigue loading stage; the crack evolution of the sample could be divided into three stages: nucleation and initiation ( ), stable expansion ( ), and unstable fracture ( ). There were distinct differences in the crack propagation modes of the rock samples with different prefabricated crack angles. The relationship between the crack initiation angle and prefabricated crack angle was analyzed based on the maximum circumferential stress theory. Moreover, with an increase in the prefabricated crack angle, the rock sample gradually changed from compression–shear failure to tension–shear failure.     

Correlation of material constraint with fracture toughness of interface regions in a dissimilar metal welded joint

In this work, the constraint parameter A_p based on crack‐tip equivalent plastic strain was calculated by finite element analyses for the cracks located at different locations in two interface regions in a dissimilar metal weld joint (DMWJ). The capabilities of the parameter A_p for characterizing material constraint and establishing correlation of material constraint with fracture toughness of the interface region cracks have been examined. The results show that the parameter A_p can characterize material constraint effect caused by material mismatch and initial crack positions in the interface regions. Based on the A_p, the correlation lines and formulae of material constraint with fracture toughness of the interface region cracks in the DMWJ can be established, and they may be used for obtaining material constraint‐dependent fracture toughness for the interface region cracks. The results in this work combining with those in the previous studies indicate that the parameter A_p may be a unified constraint parameter that can characterize both geometry constraint (including in‐plane and out‐of‐plane constraints) and material constraint, and it may be used in accurate fracture assessments of welded components with different geometry and material constraints.     

Fatigue reliability assessment of turbine discs under multi‐source uncertainties

Hot section components of aircraft engines like high pressure turbine (HPT) discs usually operate under complex loadings coupled with multi‐source uncertainties. The effect of these uncertainties on structural response of HPT discs should be accounted for its fatigue life and reliability assessment. In this study, a probabilistic framework for fatigue reliability analysis is established by incorporating FE simulations with Latin hypercube sampling to quantify the influence of material variability and load variations. Particularly, variability in material response is characterized by combining the Chaboche constitutive model with Fatemi‐Socie criterion. Results from fatigue reliability and sensitivity analysis of a HPT disc indicated that dispersions of basic variables must be taken into account for its fatigue reliability analysis. Moreover, the proposed framework based on the strength‐damage interference provides more reasonably correlations with its field number of flights rather than the load‐life interference one.     

Reduction of measured toughness due to out‐of‐plane constraint in ductile fracture of aluminium alloy specimens

It is generally believed that a lower bound on the fracture toughness of a material is obtained from a standard test, particularly in metals where yielding occurs prior to fracture. The understanding is that in such a test the material around the crack tip is highly constrained hence reducing the extent of yielding. In this paper, we report the results of fracture tests where a tensile load is applied to a biaxial aluminium alloy specimen in the direction parallel to the crack front in addition to the fracturing load normal to the crack surface. We show that in this case a lower fracture toughness is measured than that obtained from a standard test. Indeed, for the highest value of tensile load used in our tests the J‐integral at fracture was half the value measured in a standard test. It is also shown that the volume of the plastic region can be used to measure the effect of constraint, irrespective of the manner in which the constraint arises. This approach suggests an even lower fracture toughness may be obtained than that measured here in certain loading conditions.     

Fatigue strength of spring steel with small scratches

In compression coil springs subjected to cyclic load, fatigue cracks can sometimes initiate and propagate from scratch‐like small defects produced during the manufacturing process and degrade the fatigue strength. In this study, torsional and rotating bending fatigue tests were conducted to examine the fatigue behavior of a high‐strength spring steel (JIS G 3561, SWOSC‐V) in the presence of small scratches. The sensitivity of the HCF and VHCF strength to small scratches was evaluated based on the parameter model.