Standard Fracture Toughness Specimen Research Articles

Numerical investigation on the fracture driving force of laser welds and arc welds

The brittle fracture driving forces of laser beam welds (LBWs) and arc welds (AWs) are investigated and compared numerically with a center through-thickness cracked panel (CTCP) and a standard fracture toughness specimen (3-point bending specimen, 3PB). The effects of hard zone width (H) and strength mismatch ratio (Sr) were systematically studied at global strain (e∞) of 0.1% and 0.2%. It was found that the peak opening stress near the crack tip decreased with narrower H for LBW at e∞ = 0.2%, which can be ascribed to the better shielding effect provided by the softer base metal (BM) on hard zone welds. The peak normalized opening stress σyy/σY,WM was found nearly to be 3.0 for different Sr at e∞ = 0.1%, which decreased to 2.5 at e∞ = 0.2% due to more plastic deformation in the BM. The shielding effect ΔσW increased with higher Sr or narrower H. The effect of H and Sr on required CTOD fracture toughness in 3PB was also discussed basing on Weibull stress criterion. The required CTOD in 3PB of LBW can be decreased to be much lower than the AW with sufficiently narrow H. The harm effect of higher Sr on required toughness is less compared with the influence of lower H.

Numerical simulation of delamination growth in fiber reinforced polymer laminates using cohesive zone modeling

In this study, the key parameters of cohesive zone modeling, which significantly affect the accuracy in delamination problems, are examined. The study is performed on various standard fracture toughness specimens subjected to mode I, mode II and mixed mode loading. The compressive buckling of a composite laminate is then modeled and the results are validated using virtual crack closure technique. It is shown that the bi-linear interface law with identified parameters provides the best match for the standard fracture toughness specimens while for buckling delamination the effect of interface law shape and interfacial strength is substantial and cannot be ignored.

Use of notched small punch test specimens for the determination of fracture properties in structural steels

Various attempts have been made to determine the fracture toughness of metallic alloys by means of miniature tests, such as the small punch test, SPT. The use of notched SPT samples is the most convenient way to explore but as yet there is no consensus regarding the best methodology to apply. In this paper, longitudinally notched SPT samples of different steels were tested and the opening of the mouth of the notch was measured in the course of the tests, using interrupted tests to observe where the first crack appears in the most strained region of the notch region. Numerical analyses of the notch SPT tests were also performed in order to confirm the experimental results.Comparing Crack Tip Opening Displacement (CTOD) results obtained using standard fracture toughness specimens with those derived from notched small punch tests, a procedure to obtain the value of the critical CTOD, δIC, is proposed using the notch mouth opening value measured at the maximum punch displacement registered in the miniature test.

Experimental verification to determine fracture toughness from the small punch test using “Local approach”

The main tasks of the small punch (SP) technique are to derive standard material properties from a limited amount of material, including strength/toughness, creep and fatigue behaviour etc. The complicated problem of determining fracture toughness poses significant difficulties. Although many methods have been put forward to increase the prediction accuracy, no satisfactory methods are available yet. Recently, the so-called “Local approach” has been introduced to determine ductile fracture from the small punch test by means of a micro-mechanical model introduced by Gurson and modified by Needleman and Tvergaard. By using the observed load-deflection curve from the small punch test, reverse finite element analysis is performed to identify both the material plastic property (σ-ε curve) and the damage parameters of the Gurson model. With these material parameters known, a standard fracture toughness (CT) specimen is simulated by finite element analyses, from which the J-integral and the crack extension can be estimated. A J-R resistance curve can be created by multiple specimens with different load-line-displacements, and the fracture toughness JIC can be determined according to ASTM E 1820-17.In order to verify this new approach, the standard uniaxial test, the small punch tests and the standard fracture toughness tests are needed with the same material. Up to now, only a few of these kinds of experimental verification are available. In this paper, an overview on the existing methods of determination of fracture toughness from small punch test is given, and the “Local approach” for small punch test is addressed. Verifications are summarized from three high level institutes, including MMT in the Czech Republic, JRC Petten in the Netherlands and EPRI in the USA. The predicted JIC with that from standard fracture toughness tests are compared. A good agreement is found and shows that the “Local approach” is capable of predicting fracture toughness from small punch tests. The prediction accuracy by “Local approach” is better than existing methods. Further work is needed as available tests are still limited.

An evaluation of the advantages and limitations in simulating indentation cracking with cohesive zone finite elements

A cohesive zone model is applied to a finite element (FE) scheme to simulate indentation cracking in brittle materials. Limitations of using the cohesive zone model to study indentation cracking are determined from simulations of a standard fracture toughness specimen and a two-dimensional indentation cracking problem wherein the morphology of the crack and the geometry of the indenter are simplified. It is found that the principles of linear-elastic fracture mechanics can be applied when indentation cracks are long in comparison to the size of the cohesive zone. Vickers and Berkovich pyramidal indentation crack morphologies (3D) are also investigated and found to be controlled by the ratio of elastic modulus to yield strength (E/Y), with median type cracking dominating at low ratios (e.g. E/Y = 10) and Palmqvist type cracking at higher ratios (e.g. E/Y = 100). The results show that cohesive FE simulations of indentation cracking can indeed be used to critically examine the complex relationships between crack morphology, material properties, indenter geometry, and indentation test measurements, provided the crack length is long in comparison to the cohesive zone size.

Constraint-based assessment of fracture in welded components

A toughness correction method, developed as ISO 27306, specifies an equivalent crack tip opening displacement (CTOD) ratio, β, for the correction of CTOD toughness for constraint loss in structural components. Using β, the standard fracture toughness specimen and structural components are linked at the same level of the Weibull stress. This paper applies the IST method to the fracture assessment of welded components. Effects of the strength mismatch and residual stress in welds on β are implemented into the toughness correction. The strength mismatch does not have an influence on β, provided that the strength mismatch between the weld and base metals is in the range from 0.9 to 1.2. On the other hand, residual stress exerts a large influence at a low CTOD level below full yielding: β is elevated by the tensile residual stress. It is shown on the failure assessment diagram that the CTOD toughness correction with β eliminates the excessive conservatism often found in the conventional approach and leads to accurate fracture assessments of welded components.

A study on the influence of cohesive zone interface element strength parameters on mixed mode behaviour

This paper presents a detailed study of the influence of maximum interfacial stress on interface element analyses for composites delamination. The development of the non-linear cohesive zone ahead of a crack tip is analysed with respect to length, stress distribution and mode ratio. The energy absorbed by interface elements is compared with the crack tip strain energy release rate from fracture mechanics analyses. These studies are performed initially on standard fracture toughness specimens, where mode-ratio is fixed by the applied displacement constraints. Results show close agreement with linear elastic fracture mechanics solutions. A simple ply drop specimen is then modelled, where the mode ratio is not constrained by the boundary conditions, and results are compared with the Virtual Crack Closure Technique. In this case maximum interfacial stress has a far greater influence on the numerical results, due to its significant influence on cohesive zone length, mode ratio and energy absorbed.

Equivalent CTOD Concept for Correction of CTOD Toughness for Constraint Loss in Steel Weld Components

This paper presents a new fracture assessment method, IST method developed as ISO 27306. The IST method implements an equivalent CTOD ratio, β, for the CTOD toughness correction for constraint loss in structural components. Using β, the standard fracture toughness specimen and structural components are linked at the same level of the Weibull stress. This paper extends the equivalent CTOD concept to weld components. Effects of the weld strength mismatch and residual stress on β are discussed. It is shown on the failure assessment diagram (FAD) that the CTOD toughness correction with β leads to accurate fracture assessments of weld panels, whereas the conventional procedure gives much conservative results.

Constraint loss correction for assessment of CTOD fracture toughness under welding residual stress – Part II: Application of toughness correction methodology

Abstract This part II paper presents the verified results of the toughness correction methodology for welded joints of wide plates. The equivalent CTOD ratio, βr, is applied to the fracture data of the welded joints from lower to upper ductile–brittle transition temperature region. In the part I paper, βr is defined as the ratio of CTOD in the standard fracture toughness specimen to CTOD in the wide plate with welding residual stress at the same level of the Weibull stress. In this part II paper, the equivalent CTOD ratio, βr, under the welding residual stress field has been verified for assessment of constraint loss effects on CTOD fracture toughness of wide plate. Fracture assessments have been conducted by applying the methodology for “After Weld Notch” and “Before Weld Notch” type welded joints. It has been found that an excessive conservatism observed in the conventional procedure is reasonably reduced by applying the proposed methodology.

Constraint loss correction for assessment of CTOD fracture toughness under welding residual stress. Part I: Methodology using the equivalent CTOD ratio

Abstract This part I of a two-part paper presents a method of assessing the effects of welding residual stress and constraint loss on the cleavage fracture of a wide plate subjected to membrane stress based on the Weibull stress criterion. It has been found that the Weibull stress criterion is efficient for evaluating the fracture instability of wide plates with and without a welding residual stress field. The concept of an equivalent crack-tip opening displacement (CTOD) ratio β r under a welding residual stress field is introduced for assessment of constraint loss effects on CTOD fracture toughness of wide plates. The equivalent CTOD ratio β r is defined as the ratio of the CTOD in the standard fracture toughness specimen to the CTOD in a wide plate with a welding residual stress at the same level of the Weibull stress. Fracture assessment procedures using β r for wide plates are shown within the framework of the failure assessment diagram. It has been found that the excessive conservatism observed in the conventional procedure can be reduced reasonably by applying the proposed method. The companion part II of the paper presents applications of the CTOD toughness correction method using β r to the fracture test data of welded joints and verifies the proposed method in the ductile–brittle transition temperature region.

Evaluating the Onset of Tearing in Elastic-Plastic Fracture Toughness Testing Using In Situ Optical Microscopy

Abstract Fracture toughness, in the sense of material resistance to ductile tearing from an initial sharp defect, is a common metric for structural integrity assessments of engineering components. While standardized test methods are well-suited for repeatable estimation of this metric, physical observation of crack-tip opening displacement (CTOD) and tearing may provide a supplemental means of evaluating the onset of tearing with greater accuracy in ductile materials. In contrast to previously documented methods of physical CTOD measurement, in situ optical microscopy on standard sidegrooved fracture toughness specimens presents an easily implemented, cost-effective tool for observing tearing onset. As an additional benefit, quantitative measurements of CTOD from in situ optical microscopy also provide a means of cross-checking standard J-integral results as determined from load-displacement test data.

延性脆性遷移温度領域における溶接残留応力場中のき裂の脆性破壊発生評価法

This paper presents the methodology of the CTOD fracture toughness correction for wide plates' welded joints from lower to upper ductile-brittle transition temperature region. Tensile plastic zone size criterion is adopted in lower transition region. The equivalent CTOD ratio, β r , is adopted in ductile-brittle transition and upper transition region. The equivalent CTOD ratio is defined as the ratio of CTOD in a standard fracture toughness specimen to CTOD in a wide plate with welding residual stress at the same level of the Weibull stress. Fracture assessments for After Weld Notch and Before Weld Notch type welded joints have been conducted by applying the toughness correction methodology. It has been found that an excessive conservatism observed in the conventional procedure is reasonably reduced by applying the proposed methodology.

Evaluation of Residual Stress Effects on Brittle Fracture Strength Based on Weibull Stress Criterion

Abstract This paper studies the method for estimating the residual stress effects on brittle fracture of structural steel based on the Weibull stress criterion. First, brittle fracture tests were conducted for four-point bend notched specimens with and without compressive preloading. It is shown that the compressive preloading apparently decreases the critical crack tip opening displacement (CTOD). The critical CTOD of the preloaded specimen can be predicted from monotonically loaded test results based on the Weibull stress criterion. It has been found that the Weibull stress is an effective fracture parameter for brittle fracture initiation under tensile residual stress. Second, using wide plate specimens with and without welding residual stress subjected to uniform tension and three-point bend fracture toughness specimens, welding residual stresses effect on the brittle fracture strength is investigated. Experiments show that the critical CTOD of wide plate with welding residual stress is significantly smaller than that without residual stress. Constraint loss effect on CTOD of wide plate can be assessed by the equivalent CTOD ratio β. β is defined as β=δ3PB/δWP, where δ3PB and δWP are CTODs of the standard fracture toughness specimen and wide plate, respectively, at the same level of the Weibull stress. Fracture assessment result using β is shown within the context of failure assessment diagram. An excessive conservatism observed in the conventional procedure (β=1) is reasonably reduced by applying the equivalent CTOD ratio β.

溶接残留応力場中のき裂からの脆性破壊発生評価におけるワイブル応力仮説による塑性拘束補正方法

This paper studies the method for estimating the welding residual stress effect on brittle fracture of structural steel based on the Weibull stress criterion. Using wide plate (WP) specimens with and without welding residual stress, the brittle fracture tests have been conducted at -75°C. The material used is a high strength steel of 780MPa class. Welding residual stress significantly decreases the fracture force and the critical CTOD of the wide plate with welding residual stress at the onset of brittle fracture initiation. And it has been shown that the critical CTOD of the WP specimens can be predicted from fracture test results of the 3-point bend specimens without residual stress based on the Weibull stress criterion. The present paper proposes the assessment method of constraint loss effects on CTOD of wide plate with residual stress based on the equivalent CTOD ratio, βr under residual stress field. The equivalent CTOD ratio, βr is defined as the ratio, δ/δrWP,whereδandδrWPare CTODs of the standard fracture toughness specimen and wide plate with welding residual stress, respectively, at the same level of the Weibull stress.Fracture assessment results using βr are shown within the framework of failure assessment diagram (FAD). An excessive conservatism observed in the conventional procedure is reasonably reduced by applying the equivalent CTOD ratio, βr.

Method of constraint loss correction of CTOD fracture toughness for fracture assessment of steel components

This paper presents a procedure for transferring the CTOD fracture toughness obtained from laboratory specimens to an equivalent CTOD for structural components, taking constraint loss into account. The Weibull stress criterion is applied to correct the CTOD for constraint loss, which leads to an equivalent CTOD ratio, β, defined as β = δ/ δ WP, where δ and δ WP are CTODs of the standard fracture toughness specimen and the structural component, respectively, at the same level of the Weibull stress. The CTOD ratio β is intended to apply to the fracture assessment of ferritic steel components to stress levels beyond small-scale yielding. Nomographs are given to determine the β-value as a function of the crack type and size in the component, the yield-to-tensile ratio of the material and the Weibull shape parameter m. Examples of the fracture assessment using β are shown within the context of a failure assessment diagram (FAD). An excessive conservatism observed in the conventional procedure is reduced reasonably by applying the equivalent CTOD ratio, β.

Use of an atomic force microscope to measure surface deformations in polymeric systems

An atomic force microscope is used to image an unstressed sample which is subsequently stressed and re-imaged. An image analysis program is described which allows mapping of surface deformations from the images. In order to show the scope of the present analysis of deformation in plastics, three load conditions showing deformation in a glassy plastic have been selected. In the first a simple tensile load is applied and the image is obtained at low magnification. These images show the general, homogeneous deformation expected with a general elongation in the load direction, an obvious Poisson contraction in the surface plane normal to the load direction and some slight suggestion of Poisson contraction in the through-thickness direction. This loading configuration is intended to reproduce the predicted deformations to illustrate the applicability of the method under simple load conditions. The second loading condition, of a tensile specimen containing a hole, is intended to illustrate the applicability of the system to more complex loading conditions where stress concentrations modify the deformation pattern. The third loading condition is around the tip of a crack propagating in a predictable way in a standard fracture toughness specimen. These images are intended to show the usefulness of the method in characterizing deformations in a complex stress field during failure of the material.

Use of an atomic force microscope to measure surface deformations in polymeric systems

An atomic force microscope is used to image an unstressed sample which is subsequently stressed and re-imaged. An image analysis program is described which allows mapping of surface deformations from the images. In order to show the scope of the present analysis of deformation in plastics, three load conditions showing deformation in a glassy plastic have been selected. In the first a simple tensile load is applied and the image is obtained at low magnification. These images show the general, homogeneous deformation expected with a general elongation in the load direction, an obvious Poisson contraction in the surface plane normal to the load direction and some slight suggestion of Poisson contraction in the through-thickness direction. This loading configuration is intended to reproduce the predicted deformations to illustrate the applicability of the method under simple load conditions. The second loading condition, of a tensile specimen containing a hole, is intended to illustrate the applicability of the system to more complex loading conditions where stress concentrations modify the deformation pattern. The third loading condition is around the tip of a crack propagating in a predictable way in a standard fracture toughness specimen. These images are intended to show the usefulness of the method in characterizing deformations in a complex stress field during failure of the material.

Analysis of constraint in single edge notch tension specimens using the T-stress

Fracture of circumferential defects found in pipeline girth welds cannot be characterized by the J-integral alone due to a lack of in-plane constraint in the thickness direction. Finite element analyses have been undertaken to determine whether the stress field in a single edge notch tension (SENT) specimen, which is representative of the geometry and loading in a pipeline, can be represented by a two-parameter characterization based on the J-integral and the T-stress. This two-parameter stress field is then related to an equivalent J-dominant stress field found in a deeply cracked single edge notch bending (SENB) fracture toughness specimen. Thus a methodology is given to predict the toughness for a specimen described by J and T from a standard fracture toughness specimen.

Improved Wide Range Expressions for Displacements and Inverse Displacements for Standard Fracture Toughness Specimens

Abstract Wide range expressions (interpolating polynomials) for displacements for standard ASTM fracture testing specimens have been developed. The strategy was to fit displacements as a function of crack length for all the specimens using a similar form of nondimensional displacement. Different forms appear in different ASTM standards for the same or similar specimens. The criterion used to establish the degree of polynomial fit and number of significant figures for the coefficients of the polynomial was for the polynomial to agree with the best available numerical displacement solutions to within 1% or better. Once the polynomials for displacement as a function of crack length were developed, inverted forms of the specific interpolating polynomials were obtained to determine relative crack length (a/W) as a function of displacement. Since the inverted polynomial will be used in tandem with the interpolating polynomial, the inverted polynomial was fit to the interpolating polynomial and not the numerical solution for displacement. Three forms of nondimensional displacements were used to invert the interpolating polynomials. The criterion used to establish the degree of polynomial and the number of significant figures of the coefficients of the polynomial was for the predicted relative crack length to agree with the actual relative crack depth to within 0.0005W. A sensitivity analysis was performed to suggest which form of interpolating polynomial should be used for standards.

Cyclic fatigue crack growth tests on disc specimens

A ring has been designed and built in which four disc specimens containing bore cracks were subjected to fatigue conditions by continuous cycling between variable upper and lower speed limits. The behaviour of the individual cracks was found to be inconsistent. While in the majority of cases the crack growth rate was always less than that predicted by the expression d a/d N = C( ΔK) n , where C and n constants which were found from crack growth tests on standard fracture toughness specimens, an important exception was found in which a pair of cracks grew slowly over a large number of cycles before growing at a very much faster rate than that predicted. Some cracks grew much more slowly than predicted and some did not grow at all, even though minimum values of ΔK were always greater than threshold values. The circumstances which govern the different types of crack growth rate behaviour are examined using finite element analysis. It appears that, for a given specimen geometry and rotational speed, the controlling influences are the number and relative lengths of the bore cracks.