Constant Stress Intensity Factor Research Articles

Dissipation during crack growth in a viscoelastic material from a cohesive model for a finite specimen

AbstractIn the present paper, we extend results recently given by Ciavarella et al. (J Mech Phys Solids 169:105096, 2022) to show some actual calculations of the viscoelastic dissipation in a crack propagation at constant speed in a finite size specimen. It is usually believed that the cohesive models introduced by Knauss and Schapery and the dissipation-based theories introduced by de Gennes and Persson-Brener give very similar results for steady state crack propagation in viscoelastic materials, where usually only the asymptotic singular field is used for the stress. We show however that dissipation and the energy balance never reach a steady state, despite the constant propagation crack rate and stress intensity factor. Our loading protocol permits a rigorous solution, and implies a short phase with constant specimen elongation rate, but then possibly a very long phase of constant or decreasing elongation, which differs from typical experiments. For the external work we are therefore unable to use the de Gennes and Persson-Brener theories which suggested that the increase of effective fracture energy would go up to the ratio of instantaneous to relaxed modulus, at very fast rates. We show viscoelastic dissipation is in general a transient quantity, which can vary by orders of magnitude while the stress intensity factor is kept constant, and is largely affected by dissipation in the bulk rather than at the crack tip. The total work to break a specimen apart is found also to be possibly arbitrarily large for quite a large range of intermediate crack growth rates.

The Influence of Residual Stress on Fatigue Crack Growth Rates in Stainless Steel Processed by Different Additive Manufacturing Methods

The properties and microstructure of Type 304L stainless steel produced by two additive manufacturing (AM) methods—directed energy deposition (DED) and powder bed fusion (PBF)—are evaluated and compared. Localized heating and steep temperature gradients of AM processes lead to significant residual stress and distinctive microstructures, which may be process-specific and influence mechanical behavior. Test data show that materials produced by DED and PDF have small differences in tensile strengths but clear differences in residual stress and microstructural features. Measured fatigue crack growth rates (FCGRs) for cracks propagating parallel to and perpendicular to the build directions differ between the two AM materials. To separate the influences of residual stress and microstructure, K-control test procedures with decreasing and constant stress intensity factor ranges are used to measure FCGRs in the near-threshold regime (crack growth rates ≤ 1 × 10−8 m/cycle). Residual stress is quantified by the residual stress intensity factor, Kres, measured by the online crack compliance method. Correcting the FCGR data for differences in Kres brings results for specimens of the two AM materials into agreement with each other and with results for wrought specimens, when the latter are corrected for crack closure. Differences in microstructure and tensile strength have an insignificant influence on FCGRs in these tests.

Hydrogen-enhanced fatigue crack growth of martensitic stainless steel: A predictive model and experimental validation

Atomic hydrogen (H) diffusion in metallic structures affects the mechanical properties of steel alloys. However, the effect of hydrogen embrittlement on the fatigue crack propagation rate (FCGR) is not fully understood, and serious uncertainties can affect the design and inspection schedules of hydraulic turbine runners based on the defect-tolerance approach. The FCGR in a complex microstructure such as tempered martensitic stainless steel is governed by the H content, stress distribution, and microstructure at the crack tip. The synergetic interactions between these parameters should be kinetically studied as the crack propagates. In this study, an original model was proposed to predict the influence of H on the fatigue crack propagation rate. The model was developed specifically for tempered martensitic stainless steels containing austenite. Subsequently, it was validated through experiments performed on 415 martensitic stainless steel containing 20% of reformed austenite (RA). The material’s FCGR was tested in its raw condition, also after charging with H. Compact tension (CT) specimens were tested at two constant stress intensity factor ranges (ΔK = 8 MPa.m0.5 and 15 MPa.m0.5) and three cyclic loading frequencies (f = 35 Hz, 3.5 Hz, and 0.35 Hz). The results show a very good agreement with the predictions of the model. Moreover, both the model and the experimental results reveal that there is a critical ΔK that is dependent on the loading frequency at which the impact of H on the FCGR is maximum. Moreover, as predicted by the model, a decrease in the loading frequency led to an increase in the susceptibility of the FCGR to H.

Elasto-Plastic Fatigue Crack Growth Behavior of Extruded Mg Alloy with Deformation Anisotropy Due to Stress Ratio Fluctuation.

Fatigue crack growth (FCG) experiments were performed using a low-temperature extruded magnesium alloy AZ31 with texture. Under a constant maximum stress intensity factor (Kmax), the stress ratio R was changed from 0.1 to −1 during the fatigue crack growth process, and the FCG behavior before and after the R change was investigated. As a result, tensile twins were generated owing to the fatigue load on the compression side of R = −1, and the FCG velocity was accelerated. In addition, when the maximum compressive stress at R = −1 (|(σmin)R = −1|) exceeded the compressive yield strength of the material (σcy), the FCG velocity after R fluctuation greatly accelerated. On the other hand, under the condition |(σmin)R = −1| < σcy, the degree of acceleration of the FCG velocity due to R fluctuation was small. In either case, the degree of acceleration in the FCG increased as the Kmax value increased. The above FCG acceleration mechanism due to the R fluctuation was considered based on the observation of the deformation and twinning states of the fatigue crack tip, the fatigue crack closure behavior, and the cyclic stress–strain curve of the fatigue process. The FCG acceleration mechanism was as follows: First, the driving force of the FCG increased owing to the increase in crack opening displacement due to the generation of tensile twins. Second, the coalescence of the main crack and a plurality of microcracks were generated at the twin interface. The elasto-plastic FCG behavior after the stress ratio fluctuations is defined by the effective J-integral range ΔJeff.

Temperature and test specimen thickness (TST) effect on tensile and fracture behavior of AA2050-T84 alloy

AA2050-T84 is a third-generation Al-Li alloy used for primary structures of the modern transport aircraft wing. Temperature variation is common during flights, and the effect of temperature on the damage tolerance behavior of Al-Li alloys is significant. In the present work, the effect of temperature on tensile and fracture toughness of the AA2050-T84 alloy was tested experimentally. Further, the effect of Test Specimen Thickness (TST) on crack behavior is studied numerically using constraints variation. The Compact Tension (C(T)) specimen was used for linear elastic fracture analysis with variation in thickness to width ratio (B/W) as 0.1, 0.5, and 1. T11 and T33 constraint parameters were used to measure the effect of TST at −20 °C, 24 °C, and 200 °C. Increase in specimen thickness for constant stress intensity factor (KI) resulted in the decrease of T11. However, the T33 increased with an increase in specimen thickness for all temperatures considered. At −20 °C and 24 °C temperatures, the T11 variation was almost identical at all thicknesses. However, a decrease in T11 around 8% was witnessed at 200 °C compared to room temperature. The temperature effect on the T33 variation was steady and marginal. The temperature and TST effect on AA2050-T84 alloy was significant, and the present investigation results are crucial for aircraft design engineers.

Effect of Yield Strength Distribution Welded Joint on Crack Propagation Path and Crack Mechanical Tip Field.

Due to the particularity of welding processes, the mechanical properties of welded joint materials, especially the yield strength, are unevenly distributed, and there are also a large number of micro cracks, which seriously affects the safety performance of welded joints. In this study, to analyze the effect of the uneven distribution of yield strength on the crack propagation path of welded joints, other mechanical properties and residual stresses of welded joints are ignored. In the ABAQUS 6.14 finite element software, the user-defined field (USDFLD) subroutine is used to define the unevenly distributed yield strength, and extended finite element (XFEM) is used to simulate crack propagation. In addition, the static crack finite element model of the welded joint model is established according to the crack propagation path, which is given the static crack model constant stress intensity factor load, and the influence of an uneven yield strength distribution on mechanical field is analyzed. The results show that the crack length of welded joints as well as the plastic deformation range of the crack tip in high stress areas can be reduced with the increase of yield strength along the crack propagation direction. Moreover, the crack deflects to the low yield strength side. This study provides an analytical reference for the crack path prediction of welded joints.

Environmentally Assisted Cracking of Subsea Pipelines in Oil &amp; Gas Production Environments—Effect of Static Loading

Fatigue crack growth rate of line pipe steels in sour environments typically exhibits a steady-state value at low frequencies. However, in highly inhibited sour environments, there is no evidence of a steady-state fatigue crack growth at low frequencies. This is likely a result of static crack growth rate at Kmax. Stable static crack growth measured under constant stress intensity factor (K) conditions in inhibited sour environments was in the range of 10−7 mm/s to 10−8 mm/s. The crack growth rate in inhibited sour environments is likely associated with crack tip processes associated with metal dissolution/film formation and associated hydrogen evolution. The results obtained were modeled based on a crack tip strain rate based approach, where the rate limiting step was the metal dissolution/FeS formation and the corresponding hydrogen generation reaction.

Theoretical and experimental study on optimal cropping load control strategy of duralumin alloy AlCu4Mg1 based on linear elastic fracture mechanics

In this work, a metal bar fine-cropping system is designed to study the influence load control strategies based on theoretical and cropping experiments. The principle of the new cropping system and mechanical compositions system are introduced. Three different load control strategies are designed based on duralumin alloy AlCu4Mg1 bar, and the optimal loading order is determined under them. According to a new proposed cross-section quality evaluation method, the test results show constant stress intensity factor range of external load ([Formula: see text]), linear decreasing cyclic load of appropriate time coefficient ([Formula: see text]) can obtain better cropping effect and the best quality is obtained by the loading cycle ([Formula: see text]).

Experimental investigation and numerical modeling of the fatigue crack growth in friction stir spot welding of lap-shear specimen

In this research, the fatigue behavior of the friction stir spot welding (FSSW) is analyzed experimentally and numerically in the lap-shear specimens of Al 6061-T6 alloy. The micro-hardness, static and fatigue experiments are performed to investigate the mechanical behavior of the FSSW. Two fatigue failure modes are observed at different load levels, including shear fracture at high load levels and transverse crack growth at low load levels. The welding process is modeled using the coupled Eulerian-Lagrangian thermo-mechanical technique in order to predict the residual stresses. The fatigue life of FSSW is evaluated by a three-dimensional finite element re-meshing model using Zencrack software, which considers the evaluated residual stresses. Three-dimensional determined crack profile shows good agreement with the experimental fractured surface. The results of this investigation are compared with the available numerical and theoretical models and reveal better agreement with the experimental results due to the three-dimensional re-meshing modeling of crack growth and considering the residual stresses. The most previous models have considered constant kink angle and stress intensity factors during the crack growth. The results of this study approved that these assumptions are not appropriate.

A model of energy dissipation at fatigue crack tip in metals

Experimental and numerical studies investigating fatigue crack growth were conducted on flat samples made of stainless steel AISE 304 and titanium alloy Grade 2. The heat flux from the crack tip caused by plastic deformation localization was measured using the contact heat flux sensor previously developed by the authors. This provides a possibility to find a correlation between energy dissipation and crack propagation rate under fatigue uniaxial loading with constant stress intensity factor and under biaxial loading with constant stress amplitude. The experiments with constant stress intensity factor have shown a decrease in energy dissipation at constant crack rate and R=-1 (R=0). A theoretical analysis of the stress field at the fatigue crack tip has been carried out to explain this phenomenon. Based on the obtained results, the heat flux from the crack tip is represented as the sum of two functions describing energy dissipation in monotonic and reversible plastic zones separately. It has been shown that dissipation in a reversible plastic zone is a function of the applied stress amplitude only. This causes energy dissipation to decrease at constant stress intensity factor. The proposed phenomenology was successfully verified by testing both materials under biaxial loading.

Strength evaluation of butt joint by stress intensity factor of small edge crack near interface edge

Failure of the bonded dissimilar materials generally initiates near the interface, or just from the interface edge due to the stress singularity at the interface edge. In this study, the stress intensity factor of an edge crack close to the interface between the dissimilar materials is analyzed. The small edge crack is strongly dominated by the singular stress field near the interface edge. The analysis of stress intensity factor of small edge crack near the interface in bi-material and butt joint plates is carried out by changing the length and the location of the crack and the region dominated by the interface edge is examined. It is found that the dimensionless stress intensity factor of small crack, normalized by the singular stress at the crack tip point in the bonded plate without the crack, is equal to 1.12, independent of the material combination and adhesive layer thickness, when the relative crack length with respect to the crack location is less than 0.01. The adhesive strength of the bonded plate with various adhesive layer thicknesses can be expressed as the constant critical stress intensity factor of the small edge crack.

Evaluation of adhesive scarf joint strength by using singular stress field of small interface crack

In the present study, the adhesive strength of scarf joint is examined by using the stress intensity factor of the fictitious small interface crack. The stress intensity factor of small crack near the interface edge is dominated by the singular stress field of the interface corner. In this study, to evaluate the joint strength, small crack is assumed at the interface corner of the scarf joint. The stress intensity factor of the interfacial crack is calculated by changing the thickness of the adhesive layer and the scarf angle. By using the experimental fracture strength of the scarf adhesive joint specimens under tension, the values of the critical stress intensity factor are calculated. From the analysis result, when the combination of adhesive materials and the scarf angle are fixed, the critical stress intensity factors of the small interface crack are constant value irrespective of the adhesive layer thickness. Therefore, the adhesive joint strength can be evaluated as the constant stress intensity factor of small interface crack. In addition, it is possible to evaluate easily the stress intensity factor by using the dimensionless coefficients depending only on the material combination when the crack length is sufficiently smaller than the thickness of the adhesive layer. The effects of adhesive layer thickness and adhesion angle of scarf joint specimen were discussed and the effectiveness of the proposed method was indicated.

Theoretical and experimental investigation on influence of load control strategy of LY12 duralumin alloy bar fine cropping process

In present work, both the theoretical solutions and the corresponding cropping experiments are carried out to investigate the influence of the load control strategy on bar fine cropping process. The working principle of the new proposed cropping method is detailed introduced. Five different types of the loading cycles are designed basing on it. A new proposed load control strategy with a suitable assumed constant stress intensity factor range is obtained theoretically and verified by the corresponding cropping experiments. According to a new proposed cross-section quality evaluation method, the comparative results show that the section quality and the cropping time are greatly influenced by the cropping load. The best quality is obtained by the loading cycle (iii).

Influence of microstructural discontinuities on the behaviour of long cracks in the VHCF regime for the aluminium alloys EN AW 6082 and EN AW 5083

In the present study two different aluminium alloys, the precipitation hardening alloy EN AW 6082 (peak-aged and overaged) and the work-hardening alloy EN AW 5083 (soft annealed) were examined. Fatigue cracks were initiated by means of a focused ion beam notch and a longdistance microscope was used for in-situ observation of the crack growth behaviour. The crack growth was investigated at constant stress intensity factors near the threshold regime. During the insitu investigation a change in crack growth velocity was detected. It could be observed that the barrier function of grain boundaries and primary precipitations are the major reason for crack growth retardation despite the fact that the crack is in the long crack growth range. The microstructural influence becomes more important with decreasing ΔK values, meanwhile the average crack growth rate decreases simultaneously. Experimental results have shown that the Febased precipitates are influencing the crack growth rate for both aluminium alloys. Meanwhile, grain boundaries are causing a deceleration of the crack growth rate primarily in case of the work hardened aluminium alloy. This is assumed to be the reason for the smaller average crack growth rate in EN AW 5083 compared to that observed for the precipitation hardening alloy while applying comparable ΔK values.

Influence of microstructural discontinuities on the behaviour of long cracks in the VHCF regime for the aluminium alloys EN AW 6082 and EN AW 5083

In the present study two different aluminium alloys, the precipitation hardening alloy EN AW 6082 (peak-aged and overaged) and the work-hardening alloy EN AW 5083 (soft annealed) were examined. Fatigue cracks were initiated by means of a focused ion beam notch and a longdistance microscope was used for in-situ observation of the crack growth behaviour. The crack growth was investigated at constant stress intensity factors near the threshold regime. During the insitu investigation a change in crack growth velocity was detected. It could be observed that the barrier function of grain boundaries and primary precipitations are the major reason for crack growth retardation despite the fact that the crack is in the long crack growth range. The microstructural influence becomes more important with decreasing ΔK values, meanwhile the average crack growth rate decreases simultaneously. Experimental results have shown that the Febased precipitates are influencing the crack growth rate for both aluminium alloys. Meanwhile, grain boundaries are causing a deceleration of the crack growth rate primarily in case of the work hardened aluminium alloy. This is assumed to be the reason for the smaller average crack growth rate in EN AW 5083 compared to that observed for the precipitation hardening alloy while applying comparable ΔK values.

Environmentally assisted crack growth rate of an austenitic steel TP347HFG in high‐temperature medium

The crack growth rate (CGR) tests of austenitic steel TP347HFG were conducted under &lt;10‐8000 ppb dissolved oxygen (DO) in steam, the alternating environment of air and steam and supercritical water (SCW) at 600–650 °C. A constant stress intensity factor (K) method and direct current potential drop technique were used in the tests to evaluate its environmentally assisted cracking (EAC) properties as superheater and reheater boiler tubes in ultra‐supercritical power plants. CGR increases monotonically with temperature and DO content. CGR in SCW is greater than that in the high‐temperature steam which indicates that exposure pressure has an obvious effect on crack propagation. The varying CGR in different experimental environments show that exposure medium participates in the cracking process. Fracture surface and cross‐sectional surface of compact tension specimen were analyzed by scanning electron microscope. The mechanism of crack propagation in different exposure environment is further discussed.

Fatigue crack growth of a railway wheel

Abstract Typically, fatigue crack propagation in railway wheels is initiated at some subsurface defect and occurs under mixed mode (I–II) conditions. For a Spanish AVE train wheel, fatigue crack growth characterization of the steel in mode I, mixed mode I–II, and evaluation of crack path starting from an assumed flaw are presented and discussed. Mode I fatigue crack growth rate measurement were performed in compact tension C(T) specimens according to the ASTM E647 standard. Three different load ratios were used, and fatigue crack growth thresholds were determined according to two different procedures. Load shedding and constant maximum stress intensity factor with increasing load ratio R were used for evaluation of fatigue crack growth threshold. To model a crack growth scenario in a railway wheel, mixed mode I–II fatigue crack growth tests were performed using CTS specimens. Fatigue crack growth rates and propagation direction of a crack subjected to mixed mode loading were measured. A finite element analysis was performed in order to obtain the K I and K II values for the tested loading angles. The crack propagation direction for the tested mixed mode loading conditions was experimentally measured and numerically calculated, and the obtained results were then compared in order to validate the used numerical techniques. The modelled crack growth, up to final fracture in the wheel, is consistent with the expectation for the type of initial damage considered.

Threshold stress intensity factor range of a mechanically-long and microstructually-short crack perpendicular to an interface with plastic mismatch

In this study, we investigated long fatigue crack growth perpendicular to a soft-hard material interface comprising the same Young’s moduli but different yield strengths. We determined the degree of fatigue crack growth retardation attributable to the interface under the constant stress intensity factor range (ΔK) using the plasticity-induced crack closure analysis with the Dugdale model. We subsequently determined the threshold stress intensity factor range (ΔKth) under a constant stress amplitude (σa). Under a constant ΔK, the retardation degree was primary dependent on the two materials’ yield strength ratio. Under a constant σa, ΔKth was dependent on both the yield strength ratio and the distance between initial crack tip and interface.

Fracture mode identification of low alloy steels and cast irons by electron back-scattered diffraction misorientation analysis

The fracture modes of low alloy steels and cast irons under tensile and fatigue conditions were identified by electron back-scattered diffraction (EBSD) misorientation analysis in this research. The curves of grain reference orientation deviation (GROD) distribution perpendicular to the fracture surface were obtained by EBSD observation, and the characteristics of each fracture mode were identified. The GROD value of the specimen fractured in tension decreases to a constant related to the elongation of corresponding specimen in the far field (farther than 5mm away from the fracture surface). The peak exhibits in GROD curves of two smooth specimens and a notched specimen near the fracture surface (within 5mm away from the fracture surface), and the formation mechanisms were discussed in detail based on the influences of specimen geometries (smooth or notched) and material toughness. The GROD value of fatigue fractured specimen is close to that at undeformed condition in the whole field, except the small area near the crack path. The loading conditions (constant stress amplitude loading or constant stress intensity factor range △K loading) and the EBSD striation formation during fatigue crack propagation were also studied by EBSD observation parallel to the crack path.

A Simple Model of Dynamic Cleavage Producing Constant Speed Crack Propagation in a Sample of Finite Width

A simple model of dynamic cleavage under longitudinal shear deformation is analyzed as an attempt to understand how ancient lapidaries might have produced smooth cleaved surfaces. Attention is concentrated on the time signature of the load applied to the specimen in order to maintain a constant stress intensity factor (or energy release rate) at the crack tip as it propagates away from the location of the applied load at a constant speed. The analysis is also applicable to situations in which fracture requires a time dependent energy release rate. An example of the cleavage of diamond is considered.