Hutchinson-Rice-Rosengren Research Articles

Quantification of crack tip constraint effect based on the critical distance

AbstractThe effect of crack tip constraint on the fracture properties of flawed components is a critical consideration in the safety assessment of engineering structures. In this work, an approximate expression of three‐dimensional von Mises stress fields ahead of the crack tip has been derived by referring to the classic Hutchinson‐Rice‐Rosengren (HRR) solution. The critical distance rc is chosen as the constraint parameter to quantify the level of the crack tip constraint. A theoretical relationship between the parameter rc and fracture toughness JQ has been proposed. The critical constraint parameter rc can be experimentally determined by using the critical fracture toughness JQ. The experimental results of compact tension (CT) and single edge‐notched bending (SENB) specimens with different crack tip constraint levels for SA‐508 and Q345B steels successfully validate the relationship between the critical fracture toughness JQ and the constraint parameter rc. According to the test results, the critical distance rc is feasible to quantify the crack tip constraint of CT and SENB specimens with different crack tip constraint levels.

Interaction analysis between strain concentration and strain localization in cracked body

AbstractThe appearance of strain localization (SL) in front of the crack tip is a factor that promotes transition toward the fatigue crack extension mode. Therefore, to predict fatigue crack extension behavior in case multiple modes occur, it is necessary to evaluate the degree of SL. In this study, the following simulations were performed on a single‐crystal twinning‐induced plasticity (TWIP) steel: (a) SL characterization by crystal plasticity finite element method (CPFEM) analysis of a smooth specimen under tension, (b) strain concentration (SC) characterization by EP‐FEM analysis of a cracked specimen under tension, and (c) characterization of interaction results between SC and SL of a cracked specimen under tension by CPFEM analysis. A comparison of the above results found that the interaction between SC and SL was large for long cracks and a significant strain field, different from the Hutchinson, Rice, Rosengren (HRR) singular field, was formed in front of the crack tip. Therefore, a parameter was proposed to quantify the SL properties in a smooth specimen. Subsequently, a fracture‐mechanics‐like method was proposed in which the results of (b) and the introduced parameters control the results of (c).

Couple analysis of DIC and FEM to quantify strain fields and crack-flank displacements in structural materials under cyclic mixed-mode I/II fracture

Mixed mode cyclic fracture under multiaxial stress-strain state is critical for the generation of appropriate damage tolerance methodologies. To this end the elaborated approach is dedicated to full range of mixed mode loading for elastic-plastic plane problem. In this study, the digital image correlation (DIC) experimental results are represented as contours as well as radial strain distributions in the local system of coordinate centered at the current crack tip position along curvilinear crack path. As a complement to the DIC measurement, finite element (FE) modelling of the displacement and strain fields around the crack tip in the compact tension shear (CTS) specimen was performed in order to reproduce experimental mixed mode loading conditions. In this study, for comparison aim we used the conventional mechanism-based strain gradient (CMSG) and classical Hutchinson–Rice–Rosengren (HRR) plasticity theories to evaluate the coupled effect of the material plastic properties and the mode mixity on the crack tip behaviour. The new material model is implemented in a commercial finite element software package ANSYS 2021R1 using a user subroutine. The intention with this work was to complement the DIC measurements as well as acquire more detailed information about the local strain ahead of the crack tip and the crack opening. From a sensitivity analysis it has been established that the DIC value depends significantly from the location along the crack direction of the pair of points selected before and behind the crack tip. As a result of the FE calculations of strain distributions, the effects of both the fracture mode and the material properties are determined.

How to get a correct estimate of the plastic zone size for shear-mode fatigue cracks?

It was found that standardly calculated sizes of plastic zones ahead of mode II and mode III cracks during fatigue experiments close to threshold loading were very large and the stresses in the specimen net cross section without stress concentration were close to the yield stress. This represents a theoretical contradiction, since at threshold loading the plastic zones should be very small. In order to clarify the situation, results from three approaches were compared: (i) linear-elastic fracture mechanics, (ii) nonlinear Hutchinson-Rice-Rosengren (HRR) stress field and (iii) elastic-plastic finite element analysis considering nonlinear material behaviour according to the cyclic stress-strain curve. It was explained that, unlike under mode I loading, the plastic zone size should not be calculated using the applied maximum stress intensity factor (SIF). Instead, the effective SIF range needs to be used for calculation of stress fields ahead of the crack tip and, consequently the plastic zone sizes. Using these values realistic plastic zone sizes were obtained (less than 50μm). It also implies that stress in the specimen net cross section should not be calculated directly. A large part of loading applied to the specimen in terms of force or torque is transferred by fracture surfaces.

Local Deformation and Fracture Behavior of High-Strength Aluminum Alloys Under Hydrogen Influence

The local deformation and fracture behavior of high-Zn Al-Zn-Mg(-Cu) alloys under hydrogen influence were investigated by in situ tests through synchrotron X-ray tomography. Intergranular and quasi-cleavage fractures were induced by hydrogen, and strain localization by the presence of cracks was not observed by 3D strain mapping. These results suggest that the strain localization at the crack tip is smaller than the measurement limit of 3D strain mapping. The average crack-tip-opening displacements, which are one of the crack driving forces specified by fracture mechanics, directly measured from the tomographic slice were 0.14 and 0.23 μm for intergranular cracks and quasi-cleavage cracks, respectively. The crack driving forces of the intergranular and quasi-cleavage cracks were small. The local deformation behavior at the crack tips was analyzed based on fracture mechanics. The local deformation field of the crack tip, which was characterized using the Rice–Drugan–Sham (RDS) solution rather than the Hutchinson–Rice–Rosengren (HRR) solution, was located within 20 μm of the crack tip, and its size was limited. The results of this work clarify that the intergranular and quasi-cleavage crack growths are caused by small driving forces; however, this behavior is not perfectly brittle, accompanying local deformation at the crack tip.

Experimental study of unstable crack propagation velocity for X80 pipeline steel

AbstractUnstable crack propagation velocity following the failure of pipeline steel has always been a problem. In this study, differences between the existing unstable crack propagation calculation models were analysed, and the deficiencies within the crack propagation velocity models were overcome. The hardening coefficient and hardening index of the ductile material were considered, and a velocity model of unstable crack propagation of pipelines based on the Hutchinson‐Rice‐Rosengren (HRR) theory elastic‐plastic stress‐strain field and the displacement field was established. Consequently, the limit propagation velocity was obtained. In full‐scale burst test, the pipe with diameter of 1422 mm was chosen to simulate the natural gas pipeline transportation environment. Compared with the theoretical result, the error was limited in 13%. The research result solved the problem of quantifying the propagation velocity of the crack in X80 pipeline, which was significant for describing the forecast of velocity and length of unstable propagation and failure characteristics of pipelines.

Analytical approaches of creep crack initiation prediction coupled with the residual stress and constraint effect

Abstract In this work, the coupled effects of residual stress and constraint on creep damage and creep crack initiation time (CCI) were analyzed by the analytical approaches based on the ductility exhaustion model. The elastic follow-up factor, Z, as well as the reference stress method and constraint parameter Q* , were considered as part of the analytical method. The variation of hydrostatic stresses, triaxiality and multiaxial strain factor considering the constraint was discussed. The suitability of the analytical method to the conditions that coupled secondary stress and the constraint effects was then investigated. Reasonable and conservative predictions of CCI time could be obtained from the theoretical solutions when the coupled effects were taken into account within the Hutchinson-Rice-Rosengren--Riedel-Rice (HRR-RR) (initiation initially under the elastic-plastic Hutchinson-Rice-Rosengren (HRR) field and then under transient creep stress conditions, the Riedel-Rice (RR) controlled stress field) and stress intensity factor—Riedel–Rice (K-RR) control (initially by K, then by transient creep stress or Riedel–Rice conditions) controlled model when compared with finite element (FE) solutions. The K-RR solutions were more accurate when primary initial stress intensity factor K P I 1/2 , and the HRR-RR solutions were more appropriate when K P I >6 MPam 1/2 .

Theoretical and numerical analysis of creep crack initiation combined with primary and secondary stresses

In this work, the creep crack initiation time (CCI) considering the residual stress effects were investigated by numerical simulation and theoretical approaches based on the ductility exhaustion model. The redistribution of stress under the combined loading condition (i.e. the tensile residual stress generated by the pre-compressed loads and primary loads) was taken into account. The elastic follow-up factor, Z, as well as the reference stress method, was considered as part of the theoretical method. The suitability of the theoretical method to the conditions that included combined primary and secondary stresses was then investigated. Reasonable and conservative predictions of CCI time could be obtained from the theoretical solutions when the elastic follow-up factor, Z, was taken into account within the K-Riedel-Rice (K-RR) controlled model (initiation initially under the elastic K field and then under transient creep stress conditions, the Riedel-Rice (RR)) and the Hutchinson-Rice-Rosengren-Riedel-Rice (HRR-RR) controlled model (initiation initially under the elastic-plastic Hutchinson-Rice-Rosengren (HRR) field and then under RR controlled stress field) compared with finite element (FE) solutions. K-RR was more suitable when the primary stress intensity factor KIP was below 15 MPa m1/2, and HRR-RR was more accurate when KIP was beyond 15 MPa m1/2. However, RRss (initiation under the steady state creep) values were much higher than the FE solutions, but K (initiation under the elastic stress intensity factor K-controlled stress field) controlled values seriously underestimated the initiation times. HRR (initiation under the elastic-plastic HRR-controlled stress field) values underestimated the initiation time when load level KIP was less than 27 MPa m1/2, but slightly overestimated when KIP was larger than 27 MPa m1/2. The HRR-RR and HRR solutions were much close and may be a little unconservative at the high load levels (KIP > 27 MPa m1/2). The CCI time including the elastic follow-up factor Z was much more accurate than when ignoring the residual stress.

Intermediate self-similar asymptotic presentation of stress and damage fields in the vicinity of mixed mode crack tip under creep regime

Higher order asymptotic fields of stress, creep strain rate and damage of a mixed mode I/II creep crack tip are obtained and analyzed on the basis of Continuum Damage Mechanics by employing a similarity variable and similarity solution. In the paper the class of the creep mixed mode crack problems in damaged power law materials under creep-damage coupled formulation for plane strain conditions is considered. With the similarity variable and the self-similar representation of the solution for a power-law creeping material and the classical Kachanov – Rabotnov power-law damage evolution equation the near crack-tip stresses, creep strain rates and damage distributions for plane strain conditions are obtained. The approximate solutions are based on the idea of the existence of the completely damaged zone near the crack tip. The multi-term asymptotic expansions of the stress and damage fields outside the completely damaged zone are found. It is shown that the asymptotical analysis of the near crack-tip fields results in nonlinear eigenvalue problems. The technique permitting to find all the eigenvalues numerically is proposed and numerical solutions to the nonlinear eigenvalue problems arising from the mixed-mode crack problems in a power-law medium under plane strain conditions are obtained. Using the approach developed the eigenvalues different from the eigenvalues corresponding to the Hutchinson-Rice-Rosengren (HRR) problem are found. For new eigenspectra and eigensolutions obtained the geometry of the completely damaged zone in the vicinity of the crack tip is found for all values of the mixity parameter. Effect of the higher order terms of the asymptotic expansions on the near crack tip field description is elucidated. Special attention is paid to angular distributions of the stress and damage fields for mixed mode loading.

Investigation on creep crack initiation prediction considering constraint effect using constraint parameter Q

The creep crack initiation (CCI) time considering the constraint effects induced by the crack depth of P92 steel was investigated via a two-parameter theoretical approach and computational study. Finite element method (FEM) analysis was conducted on different crack-depth compact tension specimens. It indicated that the high constraint with deep cracked depth did accelerate the damage accumulation process and reduce the creep crack initiation time. Further, the variation of the constraint parameter Q under the different crack depth was rather obtained. Moreover, the constraint parameter Q was taken into account in an analytical enhancement model, i.e. the C∗-Q approach was presented to predict the CCI time from a sharp crack tip. Finally, the comparison of the CCI between the analytical slutions and FEM results was employed to verify the accuracy of the analytical approach. It could be concluded that under K-RR–controlled field (initiation initially under the elastic stress intensity factor K-controlled field and then under the transient creep stress or Riedel-Rice (RR) controlled field condition) and HRR-RR–controlled field (initiation initially under the plastic Hutchinson-Rice-Rosengren (HRR) controlled field and then under the transient creep stress condition) could conservatively and effectively characterize the CCI time. The K-RR approach was more appropriate when initial stress intensity factor K was lower than 6 MPa m1/2, and the HRR-RR approach was more accurate when K was greater than 6 MPa m1/2.

Effects of the Crack Tip Constraint on the Fracture Assessment of an Al 5083-O Weldment for Low Temperature Applications.

The constraint effect is the key issue in structural integrity assessments based on two parameter fracture mechanics (TPFM) to make a precise prediction of the load-bearing capacity of cracked structural components. In this study, a constraint-based failure assessment diagram (FAD) was used to assess the fracture behavior of an Al 5083-O weldment with various flaws at cryogenic temperature. The results were compared with those of BS 7910 Option 1 FAD, in terms of the maximum allowable stress. A series of fracture toughness tests were conducted with compact tension (CT) specimens at room and cryogenic temperatures. The parameter for the Al 5083-O weldment was evaluated to quantify the constraint level, which is the difference between the actual stress, and the Hutchinson-Rice-Rosengren (HRR) stress field near the crack tip. Nonlinear 3D finite element analysis was carried out to calculate the parameter at cryogenic temperature. Based on the experimental and numerical results, the influence of the constraint level correction on the allowable applied stress was investigated using a FAD methodology. The results showed that the constraint-based FAD procedure is essential to avoid an overly conservative allowable stress prediction in an Al 5083-O weldment with flaws.

Asymptotic Stress Field in the Vicinity of the Mixed-Mode Crack in Damaged Materials Under Creep Conditions

The creep crack problems in damaged materials under mixed mode loading under creep-damage coupled formulation are considered. The class of the self-similar solutions to the plane creep crack problems in a damaged medium under mixed-mode loading is given. With the similarity variable and the self-similar representation of the solution for a power-law creeping material and the Kachanov- Rabotnov power-law damage evolution equation the near crack-tip stresses, creep strain rates and continuity distributions for plane stress conditions are obtained. The similarity solutions are based on the hypothesis of the existence of the completely damaged zone near the crack tip. It is shown that the asymptotical analysis of the near crack-tip fields gives rise to the nonlinear eigenvalue problems. The technique permitting to find all the eigenvalues numerically is proposed and numerical solutions of the nonlinear eigenvalue problems arising from the mixed-mode crack problems in a power-law medium under plane stress conditions are obtained. Using the approach developed the eigenvalues different from the eigenvalues corresponding to the Hutchinson-Rice-Rosengren (HRR) problem are found. Having obtained the eigenspectra and eigensolutions the geometry of the completely damaged zone in the vicinity of the crack tip is found for all values of the mixity parameter.

Asymptotic Self-Similar Solution of the Creep Crack Problems in Damaged Materials under Mixed Mode Loading

The creep crack problem in damaged materials under mixed mode loading is considered. The class of the self-similar solutions to the plane creep crack problems in a damaged medium under mixed-mode loading is given. With the similarity variable and the self-similar representation of the solution for a power-law creeping material and the power-law damage evolution equation the near crack-tip stresses, creep strain rates and continuity distributions for plane stress conditions are obtained. The self-similar solutions are based on the hypothesis of the existence of the completely damaged zone near the crack tip. It is shown that the asymptotical analysis of the near crack-tip fields gives rise to the nonlinear eigenvalue problems. The technique permitting to find the eigenvalues numerically is proposed and numerical solutions of the nonlinear eigenvalue problems arising from the mixed-mode crack problems in a power-law medium under plane stress conditions are obtained. Using the approach the eigenvalues different from the eigenvalues corresponding to the Hutchinson-Rice-Rosengren (HRR) problem are found. Having obtained the eigenspectra and eigensolutions the geometry of the completely damaged zone in the vicinity of the crack tip can be found for all values of the mixity parameter.

Structural fatigue crack growth on a representative volume element under cyclic strain behavior

By introducing parameters λ and ω into the crack tip field, a unified cyclic stress and strain field was first formulated by using the Hutchinson-Rice-Rosengren (HRR) field and the Rice-Kujawski-Ellyin (RKE) field under plane stress states in the present study. On the basis of the plastic strain energy and the linear damage accumulation, two fatigue crack growth models without any artificial parameters were then proposed from a representative volume element of cyclic strain behavior. The fatigue crack growth model included parameters λ and ω which showed the effect of two singularity fields. In addition, a simplified structural fatigue crack growth model was eventually established in terms of the fatigue life of each point on the crack front and the non-self-similar shape evolution law. Finally, the predictions of models are compared with the experimental data and the agreement is found to be fairly good.

Crack Growth Rate Model under Constant Cyclic Loading and Effect of Different Singularity Fields

The effect of two singularity fields: the Hutchinson-Rice-Rosengren (HRR) fields and the Rice-Kujawski-Ellyin (RKE) fields, is investigated in the present study to discuss a former fatigue crack growth (FCG) model based on energy balance during growth of the crack. A parameter which can demonstrates the effect of different types of singularity fields is included in the crack propagation model which can predict stage-II FCG behavior independently from the basic low cycle fatigue properties. Good agreement between experimental and theoretical results is obtained.

Self-similar Solutions to the Creep Crack Problem in a Damaged Medium under Mixed Loading Conditions

The self-similar solutions to the plane creep crack problems in a damaged medium under mixed-mode loading are given. With the similarity variable and the self-similar representation of the solution for a power-law creeping material and the power-law damage evolution equation the near crack-tip stresses, creep strain rates and continuity distributions are obtained. The self-similar solutions are based on the hypothesis of the existence of the totally damaged zone near the crack tip. It is shown that the asymptotical analysis of the near crack-tip fields gives rise to the nonlinear eigenvalue problems. The technique permitting to find the eigenvalues numerically is proposed and numerical solutions of the nonlinear eigenvalue problems arising from the mixed-mode crack problems in a power-law medium are obtained. Using the approach the eigenvalues different from the eigenvalues corresponding to the Hutchinson-Rice-Rosengren (HRR) problem are found. Having obtained the eigenspectra and eigensolutions the geometry of the totally damaged zone in the vicinity of the crack tip can be found for all values of the mixity parameter.

A new method to predict fatigue crack growth rate of materials based on average cyclic plasticity strain damage accumulation

By introducing a fatigue blunting factor, the cyclic elasto-plastic Hutchinson-Rice-Rosengren (HRR) field near the crack tip under the cyclic loading is modified. And, an average damage per loading-cycle in the cyclic plastic deformation region is defined due to Manson-Coffin law. Then, according to the linear damage accumulation theory—Miner law, a new model for predicting the fatigue crack growth (FCG) of the opening mode crack based on the low cycle fatigue (LCF) damage is set up. The step length of crack propagation is assumed to be the size of cyclic plastic zone. It is clear that every parameter of the new model has clearly physical meaning which does not need any human debugging. Based on the LCF test data, the FCG predictions given by the new model are consistent with the FCG test results of Cr2Ni2MoV and X12CrMoWVNbN 10-1-1. What’s more, referring to the relative researches, the good predictability of the new model is also proved on six kinds of materials.

Crack tip fields in a viscoplastic solid: monotonic and cyclic loading

The asymptotic stress and strain field near the tip of a plane strain Mode I stationary crack in a viscoplastic material are investigated in this work, using a unified viscoplastic model based on Chaboche (Int J Plast 5(3):247–302, 1989). Asymptotic analysis shows that the near tip stress field is governed by the Hutchinson–Rice–Rosengren (HRR) field (Hutchinson in J Mech Phys Solids 16(1):13–31, 1968; Rice and Rosengren in J Mech Phys Solids 16(1):1–12, 1968) with a time dependent amplitude that depends on the loading history. Finite element analysis is carried out for a single edge crack specimen subjected to a constant applied load and a simple class of cyclic loading history. The focus is on small scale creep where the region of inelasticity is small in comparison with typical specimen dimensions. For the case of constant load, the amplitude of the HRR field is found to vanish at long times and the elastic K field dominates. For the case of cyclic loading, we study the effect of stress ratio on inelastic strain and find that the strain accumulated per cycle decreases with stress ratio.

Effect of constraint induced by crack depth on creep crack-tip stress field in CT specimens

In this paper, the effect of constraint induced by the crack depth on creep crack-tip stress field in compact tension (CT) specimens is examined by finite element analysis, and the effect of creep deformation and damage on the Hutchinson–Rice–Rosengren (HRR) singularity stress field are discussed. The results show the constraint induced by crack depth causes the difference in crack-tip opening stress distributions between the specimens with different crack depth at the same C*. The maximum opening stress appears at a distance from crack tips, and the stress singularity near the crack tips does not exist due to the crack-tip blunting caused by the large creep deformation in the vicinity of the crack tips. The actual stress calculated by the finite element method (FEM) in front of crack tip is significantly lower than that predicted by the HRR field. Based on the reference stress field in the deep crack CT specimen with high constraint, a new constraint parameter R is defined and the constraint effect in the shallow crack specimen is examined at different distances ahead of the crack tip from transient to steady-state creep conditions. During the early stages of creep constraint increases with time, and then approaches a steady state value as time increases. With increasing the distance from crack tips and applied load, the negative R increases and the constraint decreases.

Self-similar solution of a tensile crack problem in a coupled formulation

Using a self-similar variables, an asymptotic investigation is carried out into the stress fields and the rates of creep deformations and degree of damage close to the tip of a tensile crack under creep conditions in a coupled (creep - damage) plane formulation of the problem. It is shown that a domain of completely damaged material (DCDM) exists close to the crack tip. The geometry of this domain is determined for different values of the material parameters appearing in the constitutive relations of the Norton power law in the theory of steady-state creep and a kinetic equation which postulates a power law for the damage accumulation. It is shown that, if the boundary condition at the point at infinity is formulated as the condition of asymptotic approximation to the Hutchinson–Rice-Rosengren solution [Hutchinson JW. Singular behaviour at the end of a tensile crack in a hardening material. J Mech Phys Solids 1968; 16(1):13–31; Rice JR, Rosengren GF. Plane strain deformation near a crack tip in a power-law hardening material. J Mech Phys Solids. 1968; 16(1):1–12], then the boundaries of the DCDM, which are defined by means of binomial and trinomial expansions of the continuity parameter, are substantially different with respect to their dimension and shape. A new asymptotic of the for stress field, which determines the geometry of the DCDM and leads to close configurations of the DCDM constructed using binomial and trinomial asymptotic expansions of the continuity parameter, are established by an asymptotic analysis and a numerical solution of the non-linear eigenvalue problem obtained.