Effect Of Crack Tip Constraint Research Articles

Experimental Investigation of Crack Tip Constraint Effects on Fracture Assessment of API 5L X65 Steel Grade for Low-Temperature Applications (−120°C)

Experimental Investigation of Crack Tip Constraint Effects on Fracture Assessment of API 5L X65 Steel Grade for Low-Temperature Applications (−120°C)

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.

T-stresses solution and out-of-plane constraint for central cracked plate (CCP) with I-II mixed mode crack under uniaxial compression

The crack tip constraint effect should be considered in the fracture assessment of structures with cracks, and the in-plane constraint and out-of-plane constraint should be illustrated simultaneously for the three-dimensional cracks in practical engineering structures. The constraint effect of central cracked plate (CCP) specimens with I-II mixed mode crack under uniaxial compression has been investigated quantitatively in present work. The relationship between T-stress components (Tx, Ty, Txy) and in-plane constraint parameter T11 has been established. The effects of a wide range of in-plane and out-of-plane geometrical configurations (including relative crack length a/W and thickness to width ratio t/W), material parameters (including elastic modulus E and Poisson's ratio ν), crack inclination angle β and friction coefficient μ corresponding to stress intensity factors (K), in-plane constraint parameter T11 and out-of-plane constraint parameters T33 and Tz at the crack tip have been calculated and discussed theoretically and numerically. It demonstrates that the constraint parameters can effectively express the stress-strain field at the crack tip. The relative crack length a/W has an influence on the in-plane and out-of-plane constraint parameters, and the thickness to width ratio t/W mainly affects the out-of-plane constraint parameters T33 and Tz. The out-of-plane constraint parameters should be considered for long cracks. There is a loss of out-of-plane constraint under compression when t/W less than or equal to 0.9, which can be much more directly and evidently investigated through the analysis of Tz than T33. The empirical equations for KII, T11 and Tz have been obtained according to theoretical analysis and simulation results, which are convenient and effective for application.

DYNAMIC DUCTILE-BRITTLE TRANSITION AND FRACTURE TOUGHNESS MEASUREMENT OF METAL UNDER INTERMEDIATE-LOW LOADING VELOCITIES

The phenomenon of ductile-brittle transition and the measurement of dynamic fracture toughness of metallic materials under impact loading are important parts of the research on dynamic mechanical properties of metal materials. In view of the lack of understanding of ductile-brittle transition of metallic materials under impact loading and the difficulty in measuring the dynamic $J$-resistance curve of ductile materials at relative low loading rate, a method is proposed to measure the ductile-brittle transition process of 15MnTi and 11MnNiMo steels at different loading rates, and the effect of crack tip constraint on the rate change of dynamic ductile-brittle transition of the two materials, by using high-speed material testing machine and its corresponding special fixtures. The dynamic fracture toughness of 15MnTi steel under low loading rate was measured by adjusting the length of compression bar and changing the crack propagation by means of the brake of upper roller. The experimental results indicate that the CT specimen of 15MnTi steel is characterized as ductile fracture when loading velocity is lower than 0.025~m/s, and the fracture character of CT specimen of 15MnTi steel is ductile-brittle combination when loading velocity is between 0.1~m/s and 0.5~m/s, and brittle fracture of the CT specimen of 15MnTi steel starts from 0.5~m/s. The phenomenon of brittle fracture followed by ductile fracture for the CT specimen of 11MnNiMo steel occurs when the loading rate is greater than 1.5~m/s. The dynamic brittle fracture rate of 15MnTi and 11MnNiMo steels is significantly affected by crack tip constraint, and the dynamic brittle fracture rate of the material decreases obviously with the increase of in-plane constraint and out of plane constraint. It is also found that in the three-point bending tests, the fracture toughness of 15MnTi steel decreases slowly with the increase of loading rate, when the loading rate is lower than 8788~MPa$\cdot$mm/s.

Fracture properties and crack tip constraint quantification of 321/690 dissimilar metal girth welded joints by using miniature SENB specimens

By using miniature SENB specimens, the fracture properties of the materials in the region of welded metal, 321 stainless steel heat affected zone, 690 alloy heat affected zone of 321/690 dissimilar metal girth welded joints were tested. Both the J-resistance curves and critical fracture toughness of the three different materials are affected by the crack size because of the effect of crack tip constraint. Groups of constraint corrected J-resistance curves of the three materials are obtained according to J-Q-M approach. The welded metals exhibit the best fracture resistance but the worst fracture resistance is observed in the material of 690 alloy heat affected zone.

The effect of crack-tip constraint in some problems of fracture mechanics

The effect of in-plane and out-of-plane crack-tip constraint parameters, namely, the non-singular T-stress components and the parameter A, in some problems of elastic and elastic-plastic fracture mechanics is discussed. The three-dimensional crack tip stresses including the non-singular T-stress components are employed to describe the crack tip plastic zone, the failure assessment diagrams and the constraint-dependent fracture toughness for a solid with a finite notch/crack under mode I loading and different angles of surface crack growth under conditions of rolling-sliding. Theoretical and numerical aspects of the two-parameter J-A approach in elastic-plastic fracture mechanics are presented in connection with crack-tip constraint. It is shown that the parameter A can be introduced in a fracture criterion as a constraint parameter.

Specimen size effect on the ductile-brittle transition reference temperature of A508-3 steel

Fracture toughness is a key parameter for evaluating the structural integrity of reactor pressure vessels (RPV). In this paper, fracture toughness KJc of different sized RPV specimens is tested at different temperatures. Master Curve method was used to model KJc and the ductile-brittle transition reference temperature T0 is obtained. It is shown that the smaller the specimen size is, the lower the T0 value is. The small specimen is not able to completely replace the standard 1CT specimen in the irradiation surveillance program to obtain T0 and material toughness. J-Q theory is employed to study size effect and crack tip constraint effect on KJc. It is shown that Q (constraint) decreases as the specimen size decreases. A prediction model to transfer the reference temperature T0 of different specimens is developed considering constraint effect by means of Q.

Comparison of the constraint parameters in elastic-plastic fracture mechanics

To describe the effect of crack-tip constraint on the stress field for finite cracked bodies, the following most widely used constraint parameters can be employed in elastic-plastic fracture mechanics, namely, local triaxiality parameter, constraint parameter Q, the second fracture mechanics parameter A using a three-term elastic-plastic asymptotic expansion. To establish the relationship between different constraint parameters, the crack-tip stress fields are employed. Relationship between the crack-tip constraint parameters A, A2, Q and of elastic-plastic fracture mechanics is investigated.

Constraint corrected cycle-by-cycle analysis of crack growth retardation under variable amplitude fatigue loading

Various models exist to predict load interaction effects on fatigue crack growth in variable amplitude loading conditions. Stress overloads have the potential to strongly retard or even arrest a propagating fatigue crack. Whereas global analysis methods (making use of equivalent quantities) allow to describe stochastic loading scenarios, describing the effects of deterministic overloads requires cycle-by-cycle analysis techniques. Within this category, plastic zone models have proven to be effective and pragmatic in terms of calibration. Current models, however, do not account for the effect of crack tip constraint on the plastic zone size, whose estimation is a requirement. This paper develops a novel (“extended”) crack growth formulation based on the traditional plastic zone based Wheeler’s model, taking into account the effect of out-of-plane constraint (plane stress versus plane strain). Calibration of the model requires characterization of shut-off overload ratios for different stress intensity factor levels. The “extended Wheeler” model gives better agreement with experimental tests results than the original and modified Wheeler model.

Three-dimensional assessments of crack tip constraint

Crack tip constraint can be used as a means to relate the stresses at the crack tip to a measure of fracture toughness of a material. Current technique to determine crack tip constraint demonstrated in structural integrity standards are based on two-dimensional plane strain approach. This paper explores the possibility of extending the current two-dimensional crack tip constraint solutions to three-dimensional crack problems through an investigation of the asymptotic structure of three-dimensional crack tip stress fields under elastic-plastic non-hardening responses. Analysis was based on three-dimensional boundary layer formulations, combined with full-field solutions of single edge notched bend bars and centre cracked tension panels having a range of thicknesses. The fields along the crack front were examined as a function of load level and thickness. From the results, it is demonstrated that, at the crack tip (r = 0), a family of asymptotic fields develop which feature a constant stress sector directly at the crack tip. Within this sector the fields differ hydrostatically while being similar in respect of the maximum stress deviator. At the intersection with the free surface, an elastic perfectly-plastic corner field which differs from the plane stress field is shown to develop. It is shown that in these fields the level of constraint is parameterised by J/zσo, where z is the distance from the free surface. J/zσo unifies both the change in the maximum principal stress and the mean stress, as a function of thickness and deformation level from all sections of different geometry and thickness specimens. An explicit expression has been developed which demonstrated the constraint loss due to in-plane and out-of plane crack tip constraint effects, allowing a two-parameter fracture mechanics methodologies in a modified form to be extended to fully three-dimensional fields.

Some observations on failure of austenitic stainless steel: effects of in- and out of plane constraint

Modern engineering design for safety-critical structures demands meticulous failure assessments. While conventional fracture toughness parameters (e.g. JIC or KIC) are perceived as a reliable tool for characterizing the fracture behaviour of many engineering components, excessive plasticity in low-strength materials with high strain hardening capability, such as austenitic stainless steels, can change the predominant failure mode to plastic collapse. In this case, assessing the component integrity assuming fracture can introduce significant conservatism in its estimated load bearing capacity. Low constraint structures such as thin sections or sections with short cracks can suffer from plastic collapse rather than fracture but there is not a measure that can predict the change of failure mechanism. In this study, the effect of crack tip constraint in terms of the thickness and initial crack size on failure behaviour of AISI Type 316L austenitic stainless steel is studied. To this end, several single edge notched bending (SENB) specimen were manufactured with different initial crack lengths and thicknesses to account for in- (i.e. crack length) and out of (i.e. thickness) plane constraint effect. Fracture tests performed according to ASTM E1820-18 except for the sample thickness and crack lengths. The challenges for measuring the crack extension for resistance curve method as a result of deviating from the standard is discussed. The failure of the samples was also assessed by Failure Assessment Diagram (FAD). The results showed that unloading compliance extremely underestimate the crack extension in the presence of significant plastic deformation of the samples. The results also showed that the plastic collapse occurs in all samples before crack starts to grow, in the blunting regime.

Effect of constraint and latent hardening ratio on the plastic flow around a crack tip in a hardening FCC single crystal

In this work, the crack tip fields in the neighborhood of a stationary mode I crack in a hardening Cu single crystal, under tensile load was investigated. A modified boundary layer (MBL) simulation was performed with the implementation of Bassani and Wu (1991) hardening model while taking into account the crystal elastic anisotropy. The effect of latent hardening ratio (LHR) on the stress and strain fields was studied by considering three different values of LHR, q, viz. diagonal hardening (q=0) and latent hardening (q=1,1.4). In addition, the effect of crack tip constraint representing different test specimens and load conditions was examined with the inclusion of T-stress through the imposed displacement boundary condition. Important observations from this work include the suppression of kink band, presence of elastic sectors, and the occurrence of triple slip near the crack tip. The increase of T-stress suppressed the plastic strain accumulation and showed a decrease in the number of triple slip sectors near the crack tip. Whereas, the increase in q made the triple slip regions slightly prominent with wider angular spread for non-negative T. But, for negative T case, rise in q caused a suppression in the angular spread of triple slip regions. Also, the implementation of T-stress allowed for a correlation between full 3D and 2D plane strain simulations in the analysis of crack tip fields for hardening single crystals. The present study offers a comprehensive investigation of the effect of crack tip constraint and latent hardening ratio on the crack tip fields for hardening FCC single crystals.

Estimation of J-resistance curves of SA-508 steel from small sized specimens with the correction of crack tip constraint

Based on normalization method, experimental J-resistance (J-R) curves of SA-508 steel using five types of specimen configurations, such as C-shaped outside edge-notched compression (COEC), C-shaped inside edge-notched tension (CIET), miniature single edge notched bend (Mini-SENB), standard SENB and compact tension (CT) specimens are given. Great difference can be observed in these experimental J-R curves because of the various specimen configuration and dimension. The results show that, COEC specimens present the lowest J-R curves with high level of crack tip constraint, but the highest J-R curves are estimated from Mini-SENB specimens because of the lowest level of crack tip constraint they have. The classic crack tip constraint effect can explain these differences, so J-Q-M theory is applied to quantify this effect through 3D elastic plastic finite element analysis, and a family of constraint corrected J-R curves for SA-508 steel are consequently obtained, which match well with the experimental data for five types of specimen configurations with different dimensions. It is applicable to predict the J-R curves of actual cracked components as long as the crack tip constraint is determined.

Theoretical approach of characterizing the crack-tip constraint effects associated with material’s fracture toughness

The conversion problem of plane strain fracture toughness ( $$K_\mathrm{IC}$$ ) which is necessarily measured according to ASTM standards, to lower constraint applications generally existing in engineering structures, has led to extensive material and labor costs. The present paper explores and quantifies the crack-tip constraint effects by the crack-tip plastic zone to serve the prediction of material’s fracture toughness. Firstly, the approximate three-dimensional crack front displacement fields are obtained by using the variable separation method. The three-dimensional stress field is then used to predict the shape and size of the crack-tip plastic zone. Secondly, the two-dimensional in-plane and the three-dimensional out-of-plane geometric constraint effects are quantified separately, and two constraint factors, i.e., $$\alpha _\mathrm{in}$$ and $$\alpha _\mathrm{out}$$ are proposed. A series of configurations of the two-dimensional and three-dimensional crack-tip plastic zones that vary with the specimen’s geometric size (plate width, thickness, etc.) are presented, which will facilitate a better understanding of the crack-tip constraint effect. Finally, the present method is applied to elucidate the significant “thickness effect” of the X70 pipeline steel’s fracture toughness by using the out-of-plane constraint factor $$\alpha _\mathrm{out}$$ . The corresponding results are compared with the experimentally measured and FEM-predicted fracture toughness $$K_\mathrm{C}$$ . It is concluded that the parameters $$\alpha _\mathrm{out}$$ and the fracture toughness $$K_\mathrm{C}$$ can be correlated with each other, which will be beneficial to the prediction of material’s fracture toughness and the avoidance of experimental costs.

Evolution of Crack Tip Constraint in a Mode II Elastic-Plastic Crack Problem

Numerous studies have shown that crack tip constraint has an important effect on the level of conservatism when crack extension is investigated in elastic-plastic fracture mechanics. Constraint effect has been explored extensively in the past but mainly for pure mode I problems. Very few researchers have dealt with the effects of crack tip constraint on mode II or mixed mode I/II fracture in metallic materials. In this paper, the evolution of mode II constraint parameter Q in terms of applied external load is determined numerically for a test specimen under pure mode II loading. The finite element method is utilized to model the specimen and to study the range of validity of mode II constraint parameter determined from a Q—T diagram. The parameter Q calculated from the finite element simulation (or from the full field solution) is compared with the values of Q determined from the Q—T diagram. For low levels of load, the results of full field solution are shown to be consistent well with the results obtained from the Q—T diagram. However, when the external load increases significantly, the results of Q—T diagram are no longer accurate and mode II constraint parameter Q should be calculated directly from finite element results.

Effect of CT Specimen Thickness on the Mechanical Characteristics at the Crack Tip of Stress Corrosion Cracking in Ni-based Alloys

It’s important to obtain accurate stress corrosion crack(SCC) growth rate for quantitative life prediction of components in nuclear power plants. However, the engineering practice shows that the crack tip constraint effect has a great influence on the mechanical properties and crack growth rate of SCC at crack tip. To study the influence of the specimen thickness on the crack tip mechanical properties of SCC, the stress, strain and C integral at creep crack tip are analyzed under different specimens thickness. Results show that the cracked specimen is less likely to crack due to effect of crack tip constraint. When the thickness ratio B/W is larger than 0.1, the crack tip constraint is almost ineffective. Value of C integral is the largest when B/W is 0.25. Then specimen thickness has little effect on the value of C integral. The effect of specimen thickness on the value of C integral is less significant at higher thickness ratio.

Transient elastic-plastic-creep crack-tip stress fields under load-controlled loading

This paper presents transient and steady-state elastic-plastic-creep crack-tip stress fields under load-controlled loading conditions for a wide range of combinations of power-law plastic and creep materials. The crack-tip stress fields are characterized in terms of 2 parameters to accommodate the crack-tip constraint effect; the C(t)- (or C*-) integral and the βQ parameter (the Q-parameter normalized with respect to the proximity parameter to plastic collapse). For practical application, the crack-tip stress fields are re-formulated explicitly in terms of time and crack-tip stress fields for elastic-plastic and steady-state creep conditions. Comparison with detailed FE results for plane strain tension and bend specimens shows that this formulation of the crack-tip stress fields agrees well with finite element results.

Effects of lattice orientation and crack tip constraint on ductile fracture initiation in Mg single crystals

In this work, plane strain finite element simulations of cylindrical void growth ahead of a notch tip in Mg single crystals are conducted to understand the effects of lattice orientation and crack tip constraint on the ductile fracture processes. The constitutive response is represented through crystal plasticity theory accounting for both slip and twinning. Three specimens - shallow, deeply cracked single edge notch tension and deeply cracked four point bend specimens, which display increasing levels of elastic biaxiality ratio (or constraint) are considered. Also two lattice orientations, with c-axis along the thickness direction and normal to the flat surfaces of notch (referred to as A and B) are studied. It is found that void growth and coalescence in orientation A (where predominantly prismatic slip occurs) take place directly ahead of the tip and fracture resistance enhances with reduction in constraint. By contrast, orientation B shows void coalescence by inclined shear bands, displays retarded void growth and higher J at crack initiation. The ductile fracture behavior is analyzed by examining slip, porosity and mean stress development in the voided cells ahead of the notch tip.

Examination of methods for the treatment of constraint effects within the FAD approach

This paper presents results of a study focusing on the effect of crack-tip constraint on the fracture behaviour of metallic materials. The principal goal is to validate two analytical methods for the consideration of constraint effects in engineering failure assessment – the R6/FITNET approach and the IST methodology. Those methods are briefly reviewed and applied to analyse available experimental data obtained in fracture tests on various cracked geometries and for two materials. Comparing to the conventional route which incorporates fracture toughness values derived in tests on highly constrained standard specimens, both methods provide an improved (less conservative) failure assessment. However, the assessment results from both methods are shown to be strongly dependent on the Weibull exponent which determination requires a certain level of expertise in the field of fracture mechanics. Since non-conservative results are possible when assuming high values, care should be taken to ensure a proper application of the respective assessment methodology.

Crack-tip constraint analyses and constraint-dependent LBB curves for circumferential through-wall cracked pipes

The leak-before-break (LBB) concept has been widely applied in the structural integrity assessments of pressured pipes in nuclear power plants. However, the crack-tip constraint effects in LBB analyses and designs cannot be incorporated. In this paper, by using three-dimensional finite element calculations, the modified load-independent T-stress constraint parameter τ* for circumferential through-wall cracked pipes with different geometries and crack sizes has been analyzed under different loading conditions, and the solutions of the crack-tip constraint parameter τ* have been obtained. Based on the τ* solutions and constraint-dependent J–R curves of a steel, the constraint-dependent LBB (leak-before-break) curves have been constructed. The results show that the constraint τ* increases with increasing crack length θ, mean radius Rm and radius–thickness ratio Rm/t of the pipes. In LBB analyses, the critical crack length calculated by the J–R curve of the standard high constraint specimen for pipes with shorter cracks is over-conservative, and the degree of conservatism increases with decreasing crack length θ, Rm and Rm/t. Therefore, the constraint-dependent LBB curves should be constructed to modify the over-conservatism and increase accuracy of LBB assessments.