Total Stress Intensity Factor Research Articles

Comparison of the continuum damage and fracture mechanics in fatigue assessment of components containing residual stresses

In the present study, the fatigue crack growth life of standard and smooth notched specimens containing residual stresses are evaluated based on the continuum damage and fracture mechanics approaches. It is indicated that fatigue crack growth lives assessed by the continuum damage model are closer to the experimental results, with a difference of <10% in the specimens containing residual stresses. The total stress intensity factor range is used to consider the effects of residual stresses in the estimation of fatigue crack growth life based on the fracture mechanics. It is found that in existing residual stresses, the stress intensity factor is not a proper parameter to evaluate crack tip zone. Fatigue crack initiation life is experimentally obtained based on assessing variations of the slope of unloading curve in the force-displacement diagram of fatigue experiments. The cycle including a change in the slope is considered as fatigue crack initiation event. Isotropic and kinematic hardening parameters of ASTM A516 pressure vessel steel are considered in finite element analyses. Tensile residual stresses are introduced into the notched specimens by employing four-point-bending with a magnitude of around 90% of the yield stress of the material. The results indicate that at least 65% of the fatigue life of the specimens is decreased due to the presence of tensile residual stresses. Tensile residual stresses are measured using the hole-drilling technique.

Reduction in Mode-I SIF of an Edge Cracked C-Shaped Specimen Using Piezoelectric Actuator

The focus of the current research is on the feasibility of an adhesively bound piezoelectric actuator in the active repair of an edge-cracked C-shaped specimen. First, only constant uniaxial tensile loading is used to determine the Mode-I stress intensity factor. The Mode-I stress intensity factor is then examined while taking into account the actuation effect provided by the piezoelectric patch when an external voltage is applied. For an edge-cracked C-shaped specimen, the total stress intensity factor is determined analytically using the concept of the superposition principle of the linear-elastic crack problem. The outcome demonstrates a considerable decrease in the Mode-I stress intensity factor following active repair using the piezoelectric actuator. Parametric analysis has been carried out to comprehend repair performance and choose the best-sized actuators for active repair.

On the prediction of fatigue crack growth based on weight functions in residual stress fields induced by laser shock peening and laser heating

AbstractThis study deals with fatigue crack growth prediction for thin sheet AA2024 specimens with residual stresses introduced through laser shock peening and laser heating treatments. Different weight functions are used to calculate the stress intensity factor due to the presence of residual stresses. A superposition principle is used by calculating the total stress intensity factor considering the applied loads and residual stresses. The fatigue crack growth is predicted using the Paris' law based on the effective stress intensity factor range, in that the effect of residual stresses is considered by changing the total stress intensity factor ratio. It is concluded, that weight functions are a powerful tool to predict fatigue crack growth in AA2024 containing residual stress fields, as long as the gradient in the loading direction, as induced by laser shock peening and laser heating, is moderate.

Numerical Study of Fatigue Crack Propagation in a Residual Stress Field Induced by Shot Peening

Shot peening (SP) is a relatively traditional but highly effective mechanical surface treatment that produces a compressive residual stress field in a shot-peened (SPed) surface, which can effectively delay fatigue crack propagation (FCP) and prolong the service life of engineering materials and structures. A multistep analysis method was developed by combining a numerical simulation of the SP process and the LEFM-based (linear elastic fracture mechanics) superposition principle to study FCP behavior in an SP-induced residual stress field. The SP-induced residual stresses were first simulated by a symmetric cell model and then introduced into a finite element model of the CT specimen. The total stress intensity factors and stress ratios with respect to different crack lengths were calculated according to the LEFM-based superposition principle. The influences of external applied load ratios and SP conditions, including one-sided and double-sided SP, on the FCP behavior of the SPed CT specimen were investigated in detail.

Fracture analysis of superconducting composites with a sandwich structure based on electromagnetic–thermal coupled model

This paper analyzes a multilayer structure with a superconducting layer in the center and strengthening layers in the outer part. This represents a generalized structural form of multilayered high-temperature superconducting cable structures for space solar power station application. An analytical model for considering the influences of thermal–mechanical–electrical–magnetic coupling and the temperature on the stress distribution will be developed. The superposition method is used to solve the temperature distribution problem. After the temperature field is calculated, the magnetic field using a critical state model that considers the temperature effect will be developed. Finally, we analyzed the influence of material properties on the thermal and magnetically induced stress intensity factors in trapped field, zero field cooling and field cooling. Results show that the stress intensity factors induced either by thermal stress or by the Lorentz force must not be neglected. If the elastic module or the thickness of substrate layer increases, the stress intensity factor induced by thermal stress increases, while the one induced by the Lorentz force declines. Importantly, when reducing the thickness of the substrate layer, the total stress intensity factor will decrease at the early stage of heat conduction but increase at the late stage of heat conduction. This fact indicates that that thicker substrate layer is not always good from the reliability point of view.

Nearly Mode I Fracture Toughness and Fatigue Delamination Propagation in a Multidirectional Laminate Fabricated by a Wet-Layup

Five double cantilever beam specimens were tested quasi-statically to obtain a GIR resistance curve. In addition, nine double cantilever beam specimens were tested in fatigue to obtain a Paris-type relation to describe the delamination propagation rate da/dN where a is delamination length and N is the cycle number. Displacement ratios of Rd = 0.10 and 0.48 were used for five and four specimens, respectively. The specimens were fabricated by means of a wet-layup process from carbon fiber reinforced polymer plies. The interface containing the delamination was between a unidirectional fabric and a woven ply. The fracture toughness and fatigue delamination propagation protocols are outlined. The mechanical and thermal residual stress intensity factors were obtained by means of finite element analyses and the conservative M-integral along the delamination front. They were superposed to determine the total stress intensity factors. It was found that the total mode I stress intensity factor dominates the other two stress intensity factors. Thus, nearly mode I deformation was achieved. Interpolation expressions for the mechanical and thermal residual stress intensity factors were determined using three and two-dimensional fittings, respectively. Results are presented with an expression for GIR determined. Moreover, the fatigue data is described including threshold values and master-curves. These results shed light on the behavior of delamination propagation in multidirectional laminate composites.

The response of accumulated stress and microstructural refinement on cyclic deformation and associated mechanism in high strength bainite-martenite dual-phase steel

We elucidate here the response of accumulated stress and microstructural refinement on the ultra-high cyclic deformation and associated crack initiation mechanism in high strength bainite-martenite dual-phase steel, where non-inclusion induced crack initiation is the dominated failure mode. The non-inclusion induced crack initiation involved nucleation of microvoids in the coarse bainitic lath when the applied stress accumulated. The density of the microvoids increased with the accumulation of applied stress, and the microvoids that were near the grain boundary connected to form a microcrack. Failure occurred when the microcracks combined to form a macrocrack. The premise of crack propagation is that the total stress intensity factor at the crack tip is larger than granular bright facet (GBF) crack growth threshold value. A mathematical criterion is proposed for non-inclusion induced cracking. The study suggested that the probability of crack initiation is reduced when the microstructural constituent, bainitic lath, is refined.

Evaluating the Reduction of Stress Intensity Factor in Center-Cracked Plates Using Piezoelectric Actuators

Active repairs using smart materials such as piezoelectric actuators can play a significant role in reducing the crack damage propagation in engineering structures. This study analytically and numerically investigated the active repair of center-cracked plates using piezoelectric actuators. First, the stress intensity factor (SIF) for a center-cracked plate due to stress produced by a piezoelectric actuator is analytically modeled. This analytical model is obtained by applying the method of weight functions. In the second step, the solution is found for the center-cracked plate due to external loading from known linear elastic fracture mechanics. These solutions are then superimposed, taking into account the superposition principle to yield the total stress intensity factor for the integrated piezoelectric actuator to the center-cracked plate. Finally, the proposed theoretical model is verified by finite element simulation. The results indicated that the relative errors of the analytical model and the FEA results are less than 5% in all the cases studied in this paper.

Experimental investigation of the effects of aggregate size distribution on the fracture behaviour of high strength concrete

This paper examines the influence of different aggregate size distributions on the fracture behaviour of high strength concrete. Three-point bend test was performed on 63 notched beams casted using three aggregate size distributions and two water to binder ratios. The total fracture energy, GF, and critical stress intensity factor, KIC, were used to determine the fracture characteristic of concrete. The results show that the values of GF decrease substantially with increasing coarseness of aggregate grain structure, λ. Values of KIC also decreased but demonstrated only limited dependence on λ. In contrast, reducing the total w/b ratio substantially increases the value of KIC but had no measurable effect on GF.

A modified loading method for separating the effect of residual stress on fatigue crack growth rate of welded joints

AbstractA novel loading method is proposed to remove the effect of residual stress on measured fatigue crack growth rate in welded joint, using which the influence of empirical crack growth rate correlation equations on the results can be avoided. The total stress intensity factor range and the effective stress ratios corresponding to the combined effect of applied and residual stress are kept constant during the fatigue crack growth test, by changing the applied maximum and minimum loads with the increase of crack length and changes in residual stress based on the superposition rule. The feasibility of the proposed method was validated by tests of compact tension specimens containing residual stresses introduced by four‐point bending. The loading method was then applied to a test of welded compact tension specimen with coupled effect of residual stress and microstructure change on fatigue crack growth rate. The fluctuation in the separated crack growth rate reflects the effect of microstructure change on fatigue crack growth rate.

Modeling approach to evaluating reduction in stress intensity factor in center-cracked plate with piezoelectric actuator patches

Active repairs using piezoelectric actuators can play a significant role in reducing the crack damage propagation in thin plate structures. Mode-I crack opening displacement is the most predominant one in tension, and it is responsible for the failure which in turn affects the load carrying capability of the cracked structure. In addition, there are limited studies that investigated the effect of the piezoelectric actuator over mode-I active repair. In this study, the mode-I stress intensity factor for a plate with a center crack, and a bonded piezoelectric actuator was modeled using the linear elastic fracture mechanics. For this, an analytical closed-form solution is developed using the virtual crack closure technique taking into account mode-I as the only effective mode, coupling effects of the piezoelectric patch, and the singular stress at the crack tip. In addition, the total stress intensity factor was obtained by the superposition of the stress intensity factor obtained from the stresses produced by the piezoelectric actuators on the crack surfaces as the only external loads on the cracked plate and the stress intensity factor due to the far-field tension load. The proposed analytical model for mode-I stress intensity factor was verified by a finite element–based approach using ANSYS finite element software. The results demonstrated a good agreement between the analytical and finite element models with a relative error of less than 4% in all the cases studied. The results illustrated that the piezoelectric patch is efficient in reducing stress intensity factor when an extension mode of the actuator is applied. However, applying a contraction mode of the piezoelectric actuators produced negative strain which increased the stress intensity factor and thus the severity of the cracked structure and could lead to damage propagation.

Descriptions of crack growth behaviors in glass–ZrO2 bilayers under thermal residual stresses

ObjectivesThis study was intended to separate residual stresses arising from the mismatch in coefficients of thermal expansion between glass and zirconia (ZrO2) from those stresses arising solely from the cooling process. Slow crack growth experimentes were undertaken to demonstrate how cracks grow in different residual stress fields. MethodsAluminosilicate glass discs were sintered onto ZrO2 to form glass–ZrO2 bilayers. Glass discs were allowed to bond to the ZrO2 substrate during sintering or prevented from bonding by means of coating the ZrO2 with a thin boron nitrade coating. Residual stress gradients on “bonded” and “unbonded” bilayers were assessed using birefringence measurements. Unbonded glass discs were further tested under biaxial flexure in dynamic fatigue conditions in order to evaluate the effect of residual stress on the slow crack growth behavior. ResultsWhen fast-ccoling was induced, residual tensile stresses on the glass increased significantly on the side toward the ZrO2 substrate. By allowing the bond between glass and ZrO2, those tensile stresses observed in unbonded specimens are overwhelmed by the contraction mismatch stresses between the ZrO2 substrate and the glassy overlayer. Specimens containing residual tensile stresses on the bending surface showed a time-dependent strength increase in relation to stress-free annealed samples in the dynamic biaxial bending test, with this effect being dependent on the magnitude of the residual tensile stress. The phenomenon observed is explained here on the basis of the water toughening effect, in which water diffuses into the glass promoting local swelling. An additional residual tensile stress at the crack tip adds an applied-stress-independent (Kres) term to the total tip stress intensity factor (Ktip), increasing the stress-enhanced diffusion and the shielding of the crack tip through swelling of the crack faces. SignificanceResidual stresses in the glass influence the crack growth behavior of veneered-ZrO2 bilayered dental prostheses. The role of water in crack growth might be of higher complexity when residual stresses are present in the glass layer.

Multiscale fatigue crack growth modelling for welded stiffened panels

ABSTRACTThe influence of welding residual stresses in stiffened panels on effective stress intensity factor (SIF) values and fatigue crack growth rate is studied in this paper. Interpretation of relevant effects on different length scales such as dislocation appearance and microstructural crack nucleation and propagation is taken into account using molecular dynamics simulations as well as a Tanaka–Mura approach for the analysis of the problem. Mode I SIFs, KI, were calculated by the finite element method using shell elements and the crack tip displacement extrapolation technique. The total SIF value, Ktot, is derived by a part due to the applied load, Kappl, and by a part due to welding residual stresses, Kres. Fatigue crack propagation simulations based on power law models showed that high tensile residual stresses in the vicinity of a stiffener significantly increase the crack growth rate, which is in good agreement with experimental results.

Defect assessment of welded specimen considering weld induced residual stresses using SINTAP procedure and FEA

The defect assessment in butt-welded joint of ASTM A36 steel plates and 7075-T7351 aluminum alloy plates containing transverse through thickness crack was analyzed using SINTAP procedure and FEA incorporating weld induced residual stresses. Weld induced longitudinal residual stress profile can be obtained through SINTAP procedure, FEA or experimental analysis. This residual stress profile can be fitted with the trapezoidal residual stress profile available in SINTAP. For three different cases, crack length and residual stress intensity factor (SIF) are calculated and its comparison with the results obtained through FEA is plotted with respect to crack length. The stress intensity factor for mechanical loading is also plotted in the same graph. Using this graphical plot, the total SIF, including residual stress and mechanical loading, can be calculated for any particular crack size. The total SIF can be compared with the fracture toughness of the material for damage tolerance analysis. Also a failure assessment diagram is drawn for welded 7075-T7351 aluminum alloy plates with different crack sizes for as-welded (only residual stress) and mechanical loading along with the existing weld induced residual stresses to show the safety level for a particular crack size and mechanical loading.

A combined experimental/numerical study of the scaling effects on mode I delamination of GFRP

Bridging by intact fibers is an important toughening mechanism in composite materials. However, a direct experimental evaluation of its contribution is difficult to achieve and in the case of large scale bridging the thickness, h, may have an important influence on the energy release rate (ERR). In this work a semi-experimental method is adopted to quantify the effects of thickness to fracture of unidirectional glass fiber reinforced polymer (GFRP) double cantilever beam specimens in mode I fracture under monotonic loads. Several specimens with thickness in the range of h = 3.5-19 mm are tested. In two selected specimens, embedded optical fibers with an array of eight or ten wavelength division multiplexed fiber Bragg gratings were are to measure local strains close to the crack plane and employed in an inverse identification procedure to determine the bridging tractions. The results suggest that the stress at the start of the bridging zone and the crack opening displacement at its end are independent of the specimen thickness. However, the rate of change of the tractions with crack length depends on the specimen thickness. While the initiation value of the ERR is independent of h, at the steady state it varies from 900 (h = 3.5 mm) to 21 00 J/m(2) (h = 19 mm). Using the identified tractions, the total stress intensity factor (SIF) and the corresponding ERR are calculated. The results show that the SIP approach gives similar results. Thus thickness, via the bridging fibers, is responsible for the effects on steady state ERR observed in the specimens used herein. (C) 2013 Elsevier Ltd. All rights reserved.

The Influential Factors Analysis of Surface Crack Propagation Behavior of ZrB2-20%SiC-10%AlN Ceramic Subjected to Thermal Shock

The indentation-quench method for investigating surface crack propagation has been studied through both experiments and model. The influential factors for surface crack propagation such as specimen thickness, thermal fatigue property, and quench temperature difference (ΔT) and one single specimen being used throughout a whole test ΔTwere surveyed in this paper. Practical results were obtained for ZrB2-20%SiC-10%AlN (ZSA) ultra-high temperature ceramic. The percentage crack growth versus ΔTcurves showed stable crack growth in a relative low ΔTinterval and unstable crack growth above a certain ΔT, and these regimes were sensitive to the thickness. The total stress intensity factor (KI) combining residual stress and thermal stress considering dynamical behavior during the quenching test was calculated by a surface crack theoretical model, the result of calculation was analyzed influential factors and crack propagation .

Studies of mode I delamination in monotonic and fatigue loading using FBG wavelength multiplexing and numerical analysis

Bridging by intact fibers in composite materials is one of the most important toughening mechanisms. However, a direct experimental assessment of its contribution is not easy to achieve. In this work a semi-experimental method is proposed to quantify its contribution to fracture of unidirectional carbon fiber/epoxy double cantilever beam (DCB) specimens in mode I delamination under monotonic and 1 Hz fatigue loads. In each specimen, an embedded optical fiber with an array of eight wavelength-multiplexed fiber Bragg gratings is used to measure local strains close to the crack plane. The measured strain distribution serves in an inverse identification procedure to determine the tractions in the bridging zone in monotonic and fatigue loads. These tractions are used to calculate the energy release rate (ERR) associated with bridging fibers. The results indicate that the ERR due to bridging is about 40% higher in fatigue. The bridging tractions are further included in a cohesive element model which allows to predict precisely the complete load displacement curve of monotonic DCB tests. Using the principle of superposition and the identified tractions, the total stress intensity factor (SIF) is calculated. The results show that the SIF, at initiation, is very close to the one calculated at crack propagation and bridging by intact fibers is responsible for the entire increase in toughness seen in the DCB specimens used herein.

Acoustic emission during tensile deformation of pre-strained nuclear grade AISI type 304 stainless steel in the unnotched and notched conditions

Acoustic emission (AE) generated during tensile deformation of notched specimens with varying notch lengths has been compared with those from unnotched specimens of a nuclear grade AISI type 304 stainless steel in the 5 and 30% pre-strained conditions. The results indicate that (a) nature of AE generation is different for different stages of deformation and (b) amount of cold work or pre-strain influences the magnitude of such AE generation. The observed results have been explained using the phenomena of varied localized deformation at the notch tip and deformation-induced α′-martensite formation in cold worked AISI type 304 stainless steel. An examination of the correlation between total AE counts (N) and stress intensity factor (K) has shown that the value of the exponent (m) in the relationship N = AKm decreases with increasing pre-strain. The formation of α′-martensite in unnotched specimens has been confirmed by equivalent δ-ferrite (%) content measurements. The examination of fracture surfaces by scanning electron microscopy (SEM) has indicated that the localized plastic deformation at the notch tip depends on the level of pre-strain.

Prediction of fatigue crack growth under constant amplitude loading and a single overload based on elasto-plastic crack tip stresses and strains

It is generally accepted that the fatigue crack growth (FCG) depends mainly on the stress intensity factor range (Δ K) and the maximum stress intensity factor ( K max). The two parameters are usually combined into one expression called often as the driving force and many various driving forces have been proposed up to date. The driving force can be successful as long as the stress intensity factors are appropriately correlated with the actual elasto-plastic crack tip stress–strain field. However, the correlation between the stress intensity factors and the crack tip stress–strain field is often influenced by residual stresses induced in due course. A two-parameter (Δ K tot, K max,tot) driving force based on the elasto-plastic crack tip stress–strain history has been proposed. The applied stress intensity factors (Δ K appl, K max,appl) were modified to the total stress intensity factors (Δ K tot, K max,tot) in order to account for the effect of the local crack tip stresses and strains on fatigue crack growth. The FCG was predicted by simulating the stress–strain response in the material volume adjacent to the crack tip and estimating the accumulated fatigue damage. The fatigue crack growth was regarded as a process of successive crack re-initiations in the crack tip region. The model was developed to predict the effect of the mean and residual stresses induced by the cyclic loading. The effect of variable amplitude loadings on FCG can be also quantified on the basis of the proposed model. A two-parameter driving force in the form of: Δ κ = K max ,tot p Δ K tot ( 1 - p ) was derived based on the local stresses and strains at the crack tip and the Smith–Watson–Topper (SWT) fatigue damage parameter: D = σ maxΔ ε/2. The effect of the internal (residual) stress induced by the reversed cyclic plasticity manifested itself in the change of the resultant (total) stress intensity factors controlling the fatigue crack growth. The model was verified using experimental fatigue crack growth data for aluminum alloy 7075-T6 obtained under constant amplitude loading and a single overload.

A study of the stress ratio effects on fatigue crack growth using the unified two-parameter fatigue crack growth driving force

A unified two-parameter fatigue crack growth driving force model was developed to account for the residual stress and subsequently the stress ratio effect on fatigue crack growth. It was found that the driving force should be expressed as a combination of the maximum stress intensity factor, K max, and the stress intensity range, Δ K, corrected for the presence of the residual stress. As a result, the effects of residual stresses manifest themselves in changes of the applied maximum stress intensity factor and the applied stress intensity range. A two-parameter function of the maximum total stress intensity factor, K max,tot, and the total stress intensity range, Δ K tot, was proposed to model the fatigue crack growth rate data obtained at various R-ratios. Based on the analysis, the unified two-parameter driving force, Δ κ = K max,tot p Δ K tot ( 1 - p ) , was derived accounting for the mean stress or the stress ratio effect on fatigue crack propagation. It was shown that the two-parameter driving force, Δ κ = K max,tot p Δ K tot 0.5 , was capable of correlating fatigue crack growth data obtained under a wide range of load ratios and fatigue crack growth rates spanning from the near threshold to the high growth rate regime. The model was successfully verified using a wide range of fatigue crack growth data obtained for Al 2024-T351 aluminium alloy, St-4340 steel alloy and Ti–6Al–4V titanium alloy with load ratios, R, ranging from −1 to 0.7.