Onset Of Crack Extension Research Articles

A Review of the Proposed K Isi Offset-Secant Method for Size-Insensitive Linear-Elastic Fracture Toughness Evaluation

Abstract Recently proposed modifications to ASTM E399, Standard Test Method for Linear-Elastic Plane-Strain Fracture Toughness KIc of Metallic Materials, would provide a new size-insensitive approach to analyzing the force-displacement test record. The proposed size-insensitive linear-elastic fracture toughness, KIsi, targets a consistent 0.5-mm crack extension for all specimen sizes by using an offset secant that is a function of the specimen ligament length. With intent to increase flexibility in the test method, the KIsi evaluation method removes the Pmax/PQ criterion, which can penalize materials with rising tearing resistance curves, and increases the limits on specimen deformation, which allows more plasticity at the crack tip at the onset of crack extension. The primary motivation for this investigation is to confirm the validity of this new interpretation of the force-displacement test record in regard to the increase in acceptable specimen deformation. This article summarizes a finite element study of the effects of increased crack tip plasticity on the KIsi evaluation method, with two primary points of investigation: the continued validity of linear-elastic fracture mechanics (LEFM) to describe the crack front conditions and the effect of crack tip plasticity on compliance change in the force-displacement record. The analytical study illustrates that LEFM assumptions remain valid at the increased deformation limit; however, the influence of plasticity on the compliance change in the test record is problematic. A proposed revision to the validity criteria for the KIsi test method is described.

Direct observation of the thickness effect on critical crack tip opening displacement in freestanding copper submicron-films by in situ electron microscopy fracture toughness testing

We evaluated the thickness effect on fracture toughness in freestanding Cu films with thicknesses of approximately 100, 500, and 2600 nm, on the basis of crack tip opening displacement (CTOD) concept by means of in situ (field emission scanning electron microscopy) FESEM and (transmission electron microscopy) TEM fracture toughness testing. During testing, an acute pre-crack tip blunted gradually and necking deformation in the out-of-plane direction occurred in the region ahead of the crack tip in all the specimens. A crack then initiated from the pre-crack tip and propagated along the necking region resulting in chisel point fracture. Since the small scale yielding condition was not satisfied in the 500 and 2600 nm specimens, the critical CTOD, $$\delta _\mathrm{i}$$ , at the onset of crack extension was directly evaluated from the in situ images. The results indicate a clear thickness effect on $$\delta _\mathrm{i}$$ (i.e. $$\delta _\mathrm{i}$$ decreases as the thickness decreases). Normalized critical CTOD, defined as $$\delta _\mathrm{{i}}/B$$ (where $$B$$ is the thickness), of 100 and 500 nm specimens are similar, $$\delta _\mathrm{{i}}/B = 1.6$$ . This suggests the presence of a fracture criterion, $$\delta _\mathrm{{i}} = 1.6B$$ , in the submicron scale regardless of the film thickness. On the other hand, $$\delta _\mathrm{{i}}/B$$ of the 2600 nm specimen was roughly half of those of the 100 and 500 nm specimens.

Fracture of Edge Cracked Layered Plates Subjected to In-plane Bending

Layered structures are used in protection systems such as personal and heavy armor, windshields and also in functionally graded thermal barriers. The focus of this study is to understand the behavior of cracks in such systems, especially when the crack orientation is such that there are property changes along the crack front. Layered plates were prepared by bonding together sheets of epoxy and Polymethylmethacrylate (PMMA) using an epoxy adhesive. Among the two, epoxy has higher elastic modulus and lower fracture toughness compared to PMMA. Two different layer configurations; a single sheet of epoxy bonded to a single PMMA sheet (two layer) and a single sheet of epoxy sandwiched between two PMMA sheets (three layer) were considered. Single edge notched specimens were loaded in three point bending and the thickness averaged stress intensity factor (SIF) was estimated through photoelasticity. Subsequently, the behavior of crack-extension in these plates was also investigated. In both configurations, crack growth initiated in the epoxy layer first and extended stably before the start of crack extension in the PMMA layer. Once the crack extension started in the PMMA layer, the plate looses its structural integrity. It was observed that the onset of crack extension in the epoxy layer can be predicted using the thickness averaged SIF. A method using analysis of patched cracks is presented for estimating the load at which the plate completely looses its load carrying capacity. The estimates from this method match well with experimental results.

In-Situ SEM J-Testing and Crack-Tip Micromechanics of Zircaloy-4 by Three-Point Bending

A three-point bend fixture has been designed, fabricated, and utilized to demonstrate the feasibility of performing in-situ J-testing at ambient and elevated temperatures inside a scanning electron microscope (SEM). Using the three-point bend test technique, in-situ SEM J-testing has been performed to measure the crack mouth opening displacement and crack extension as a function of the applied load in order to generate J-R curves for Zircaloy-4 at 25°C and 316°C. Once the J-R curve is determined, an equivalent KJ-resistance (KJ-R) curve is computed on the basis of a relationship between the J-integral (J) and the stress intensity factor (K). The J-R and KJ-R curves of Zircaloy-4 exhibit a rising R-curve behavior, while the elastic K-R curve underestimates the fracture resistance of Zircaloy-4 once substantial crack extension has occurred. For the specimen dimensions considered, the J-R curves generated by in-situ SEM J-tests are not sensitive to the specimen geometry and measure the actual fracture resistance of the material. Furthermore, the onset of crack extension is dictated by the emission of one or more slipbands from the crack tip, and a change in the crack-tip displacement field, followed by void formation along the slipband, and linkage of the voids with the main crack.

６０８２アルミニウム合金溶接材の各部の破壊靭性

The effects of Mn addition on toughness of welded Al–Mg–Si alloys have been investigated. In-situ SEM observations of fracture toughness tests have also been used to characterize crack initiation and propagation behavior through the weldment. Recrystallization of HAZ is completely suppressed by adding Mn, while a sample without Mn exhibits recrystallized coarse grain structure. Recrystallization in HAZ can lead to drastic decrease of its fracture toughness comparing with the samples containing Mn. Many microcracks are distributed at grain boundaries within several mm ahead of a crack-tip where crack-tip stresses are relatively weak. Fracture-mechanical analysis reveals that the toughness degradation is attributed to such premature damage evolution before the onset of crack extension. However, the microcracking is not attributed to so-called liquation cracks, but degradation of the grain boundaries due to the formation of film-like Al–Mg intermetallic compounds. The microcracks ahead of the crack-tip aligned at an angle of approximately 60° from an initial notch direction. Tension obliquely applied to the HAZ next to welding pool appears to give rise to such inclination of the microcracks. It is suggested that the toughness degradation can be suppressed by utilizing such anisotropy even if the GB films are formed during welding.

Propagation and Arrest of Fatigue Cracks from a Precrack under Cyclic Torsional Loading in Medium-Carbon Steel.

Fatigue tests of crack propagation from a pre crack in thin walled tubular specimens made of a medium carbon steel were performed under cyclic torsion with and without superposed static tension. The condition of the transition from shear to tensile mode and the propagation behavior during this transition were investigated from the viewpoint of fracture mechanics. The direction of fatigue crack propagation follows the direction of the maximum of the total range of the tangential stress, Δσθ max near the crack tip and then gradually changes to the direction perpendicular to the maximum of the total range of the principal nominal stress. The propagation rate is faster than the uniaxial data when compared at the onset of crack extension and at high stress intensity factors. The former acceleration is caused by crack closure and the latter acceleration is due to the non singular T stress. The negative nonsingular stress induces excessive plasticity ahead of the fatigue crack, and then accelerates the fatigue crack.

The effect of crack location and maximum stress position on the failure of a cracked piping system

The failure of a circumferentially cracked stainless steel piping system can be predicted by assuming that failure conforms to a net-section stress criterion, using as input an appropriate value for the critical net-section stress together with a knowledge of the anticipated loadings. The usual procedure is to calculate the stress acting on the cracked section via a purely elastic analysis based on the piping system being uncracked. However (a) the piping is built-in at the system ends into a larger component, and (b) the onset of crack extension requires some plastic deformation. Consequently, use of the net-section stress approach to predict the onset of crack extension, can give overly conservative failure predictions. Earlier work by the author has quantified the extent of this conservatism, and has shown how it depends on the material ductility and the geometry of the cracked section. It has also been demonstrated that the extent of conservatism depends on the elastic flexibility of the system, and in particular on the location of the cracked section within the system. The present paper extends these earlier studies, and shows that the location for which crack extension is favoured is not necessarily that location where the stress (calculated on the basis of an uncracked system analysis) is a maximum, as is implicitly assumed when the net-section stress approach is used.

Damage Field Ahead of a Tensile Crack in an Elastic-Plastic and Viscoplastic Material

This paper investigates the interaction between a macroscopic crack and microscopic damage in an elastic-plastic and viscoplastic material subjected to tensile in-plane loading. The aim is to predict the fracture conditions by accounting for void accumulation in the vicinity of the crack-tip. A power law relates the stress to the strain of the material. The damage, which invokes the growth and coalescence of microvoids, is confined to a small circular zone surrounding the crack-tip. At the onset of crack extension, the applied stress for small-scale and large-scale yielding solutions is found to be proportional to a0 -1/(n+1), where 2a0is the initial crack length and n is the strain hardening exponent of the material. For small-scale yielding, the conditions required for fatigue crack growth and steady-state creep are determined. In particular, the variations of the normalized crack length with the number of loading cycles and the time required for failure are shown for various strain hardening exponents, applied loading, and material damage parameters.

Experimental Justification for Proposed Changes to the Measurement of KIc Using ASTM E 399

Abstract During the past five years considerable effort has been devoted to developing a fracture toughness measurement standard that combines the linear elastic stress intensity factor at the onset of crack extension, KIc, and the elastic-plastic fracture toughness measurement quantities, namely, JIc, the J resistance curve (J-R curve), and the corresponding crack tip opening displacement resistance curve (CTOD-R curve). The objective of this effort was to allow the engineer to start with one specimen geometry, conduct a specified test, develop either a KQ or a JQ−R curve, and then, after application of the relevant size requirements, obtain a valid fracture toughness result. At present, different specimens are required by E 399 and E 1737 (the combination and replacement of E 813 and E 1152), and if the engineer uses the E 399 specimen geometry and test procedure and subsequently finds that the measured KQ fails the E 399 size requirements, new specimens must be machined and tested according to E 1737 to obtain valid fracture toughness measurements. This paper describes experimental tests that have been conducted in parallel with the development of the new ASTM Standard E 1820-97, a combined fracture toughness test standard that is intended to address this problem. These experimental results show that the standard J integral specimen, incorporating load line crack mouth opening displacement measurements and side grooves, can be used to obtain KIc as presently defined by ASTM E 399. The use of larger a∕W ranges is also supported by these results as long as the basic size requirements of E 399 are met and applied to both the specimen crack length and remaining ligament as well as to the specimen gross thickness.

The conservatism of the net-section stress procedure for predicting the failure of cracked piping systems: the effect of crack shape complexity on the degree of conservatism

The failure of circumferentially cracked steel piping is often predicted by assuming that failure conforms to a net-section stress criterion using as input an appropriate value for the critical net-section stress together with a knowledge of the anticipated loadings. The stress at the cracked section is usually calculated via a purely elastic analysis based on the piping being uncracked. However, because the piping is built-in at the ends into a larger component, and since the onset of crack extension requires some plastic deformation, use of the net-section stress approach can give overly conservative failure predictions. In earlier work, the author has quantified the extent of this conservatism, and has shown how it depends on the geometry of the cracked section, the material ductility and the elastic flexibility of a piping system. This paper quantifies the conservatism with regard to the case where a through-wall crack extends over a prescribed fraction of the pipe circumference, while there is also an internal circumferential crack extending around the remainder of the pipe section. This is an extreme form of circumferential cracking but, nevertheless, simulates the well-known Duane Arnold safe-end crack.

Crack growth resistance methodologies for austenitic stainless steels

The paper reviews the methodologies that are being used to quantify the effect of cracks in austenitic stainless steel structures. As a framework for discussion, these methodologies, i.e. net-section stress and tearing modulus, used to describe respectively the onset of crack extension and crack stability, are considered with regard to the behaviour of a circumferential through-wall crack in a piping system.

Toughening mechanisms in titanium aluminides

The relevant toughening mechanisms in two-phase titanium aluminides are reviewed in order to elucidate microstructure/fracture toughness relationships. Both intrinsic and extrinsic toughening mechanisms are present in Ti3Al- and TiAl-base alloys. The former affects the initiation toughness(i.e., KIC value) at the onset of crack extension, while the latter leads to crack growth toughness by instigating a resistance-curve behavior. Intrinsic toughening arises from matrix slip and ductile-phase blunting. In contrast, extrinsic toughening originates from crack deflection, ductile-phase bridging, shear ligament toughening, microcrack shielding, twin toughening, and the growing crack singularity. The influence of microstructure on toughening mechanisms in two-phase Ti3Al- and TiAl-base alloys is discussed, with particular emphasis on the need to control the microstructure in order to achieve the desired mechanical properties.

The effect of intermediate graphitization on the mechanical and fracture behavior of 2-D C/C composites

Impregnation and recarbonization effectiveness during the processing of carbon-carbon composites is largely enhanced by subjecting them to intermediate graphitization cycles. The effect of an intermediate graphitization cycle on the fracture toughness of a 2-D C/C composite has been investigated. Two materials have been considered. Both composites are reinforced with plain woven fabrics of carbon yarns, and their matrices are derived from the same resin. The only difference is that one of the composites has undergone an extra intermediate graphitization cycle. Flexural tests were conducted on multiple geometrically identical, un-notched and notched specimens of each composite in the translaminar and crosslaminar directions. The current study reveals that an intermediate graphitization has increased the fracture toughness of the C/C composite by about one fold, as measured by both the critical energy release rate at the onset of crack extension, GP ic , and the critical value of the J integral, J ic . This is accompanied by about a 25% loss in the translaminar flexural strength and a 25% decrease in the translaminar stiffness. A considerable decrease in the notch sensitivity of the C/C composite under investigation is also observed. The increase in the fracture toughness due to the intermediate graphitization of the C/C composite is also manifested in a more diffusive fracture path. The intermediate graphitization has also decreased the crosslaminar flexural strength by about 23% and the crosslaminar flexural modulus by about 15%.

Comments on the Problem of Crack Extension From a Defect in a Weld

The paper discusses the problem of crack extension in a weld in an engineering structure, and how this relates to crack extension in a small specimen of weld material. For the case where the parent material is softer than the weld material, it is argued that the J integral crack growth resistance curve for the small specimen can be above that for the structure, for which the curve depends on the flow properties of both the weld and parent materials, and also the crack size and weld thickness. The onset of crack extension can be conservatively predicted using the weld material’s toughness properties and the parent material’s flow properties, but nonconservative results may arise if the same approach is used to make instability predictions. The focus of attention is the case where the weld crack is parallel to the plane of the weld, a situation for which the J integral is path-independent with regard to any contour surrounding a crack tip.

The value of the J-integral at the onset of crack extension from a weld defect: weld material is harder than parent material

The paper addresses the problem of crack extension in a weld in an engineering structure for the case where the weld crack is parallel to the plane of the weld, a situation for which the J-integral is path independent with regard to any contour surrounding a crack tip. Assuming that crack extension is associated with the attainment of a critical crack tip opening displacement δw, a theoretical analysis based on the strip yield representation of plastic deformation shows, for the case where the weld material is softer than the parent material, how the relation between the value of J at the onset of crack extension and δw depends on the flow properties of the weld and parent materials, the crack size and the weld thickness.

The effect of residual stresses on the onset of crack extension in an engineering component

A simple theoretical model is used to demonstrate the extent to which a residual tensile stress reduces the applied stress needed to extend a crack. The conclusions are relevant to the behaviour of a weld crack in a non-stress-relieved engineering structure that is subjected to an overload.

The conservatism of the net-section stress criterion for the failure of cracked stainless steel piping

A standard procedure for predicting the failure of cracked stainless steel piping is based on the assumption that failure conforms to a net-section stress criterion, using as input an appropriate value for the critical net-section stress, together with a knowledge of the anticipated loadings. The stresses at the cracked section are usually calculated via a purely elastic analysis based on the piping being uncracked. However, because the piping is built-in at its ends into a larger component, and since the onset of fracture at a crack tip requires some plastic deformation, use of the net-section stress approach can lead to conservative failure predictions. This paper examines the extent of this conservatism, and shows that the degree of conservatism depends on the material ductility and a length parameter L∗, which is a measure of the elastic flexibility of a piping system. With a sufficiently ductile material and with a stiff piping system, definite advantages can be gained from allowing for the built-in characteristics of a piping system and for plasticity at the cracked section. There is an additional measure of conservatism due to the fact that unstable failure need not necessarily be associated with the onset of crack extension.

The value of the J-integral at the onset of crack extension from a weld defect: Weld material is softer than parent material

The value of the J-integral at the onset of crack extension from a weld defect: Weld material is softer than parent material

静的および衝撃三点曲げ試験によるアルミナの破壊じん性評価

The static and impact three point bending tests were carried out to evaluate the fracture toughness of alumina. A precrack was introduced into the specimen by BI method. In order to eliminate the influence of residual stress caused by the roughness of the crack surface, a notch was made on the crack with diamond cutter, leaving the crack tip.The static fracture toughness was evaluated by SEPB method. Because of rising R-curve behavior of alumina, the fracture toughness calculated from the maximum load would be greater than the inherent one. In this experiment, the fracture toughness was calculated from the load at the onset of crack extension, which was detected by the output of a strain gage glued near the crack tip. This value was almost the same as the fracture toughness obtained by IF method. In addition, the relation between load and strain near the crack tip observed in the static three point bending test was explained by using a simple model.In the impact three point bending test, the impact forces were loaded on the specimen by dropping a cylindrical bar from various heights. It was found that the fracture toughness had a tendency to increase with an increase of impact velocity. Furthermore, the time variation of dynamic stress intensity factor measured in this test was compared with the calculated value by a simple evaluating method which was proposed in the previous paper. As a result, both values showed good agreement until the crack began to extend.

Experimental and finite element studies on mode I and mixed mode (I and II) stable crack growth—II. finite element analysis

Finite element studies are presented on both mode I and mixed mode stable crack growth under static loadings through an aluminium (D16AT) alloy. A COD based criterion has been used to predict the load-displacement diagram from initiation to instability. The theoretical predictions are compared with experimental results presented in Part I. Results on computed crack profiles, stress-strain distribution ahead of the crack tip, J integrals, J resistance curves, plastic zones, etc., are included. The study indicates that the load-displacement diagram associated with a mixed mode stable crack growth in a compact tension type of specimen geometry can be predicted reasonably accurately using the criterion of a fixed crack opening displacement at a finite distance behind the crack tip provided the crack is allowed to grow in the direction of initial growth in the finite element analysis. The crack assumes a more blunted profile in a mixed mode than in the mode I at all the stages of stable extension. The distributions of normal stress and strain in the direction perpendicular to the crack extension line, ahead of the current crack tip, have similarities between the mode I and mixed mode, irrespective of loading angle. Both the stress and strain levels increase as the crack extension proceeds. In a mixed mode, the J integral at the onset of crack extension is the lowest compared with the values at the later stages of the extension. Further, the tearing modulus associated with initial kinking is very small; it becomes close to the mode I values at the later stages. The tearing modulus remained approximately constant during the whole mode I stable growth and it had a similar trend subsequent to kinking in a mixed mode. The specific work of crack extension is zero as Δa → 0 and it increases gradually with Δa irrespective of the mode of loading; the actual variation depends on the loading angle. The plastic zone size grows as the stable extension progresses; the growth is approximately the maximum along the crack extension line.