Effect of yield stress and specimen size on the position of fracture toughness peak (FTP) in Ji-a/W curves

Early work showed that there was a fracture toughness peak (FTP) as the fracture toughness changed with crack length/specimen width (a/W). It could be thought of as a “safe crack” for the cracks whose length is smaller than that where the FTP is located. In the present paper, it is indicated that the crack length of FTP isJ_i-a/Wcurves decreases with increasing yield stress of material and specimen size and decreasing test temperature. The reason for the fracture toughness being insensitive to the (a/W) for the ultra-high strength and brittle material is explained.     

On the ratio (Φ) of the J-integral to the total work done per unit uncracked area

The ratio (Φ) of the J-integral to the total work done per unit uncracked area is shown to be dependent upon Poisson's ratio (v) in both plane stress and plain strain conditions. An expression for Φ in three-point-bending of linear elastic materials is derived analytically as a function of a/W (initial crack size/width), S/W (span/width) and v. The variation of Φ on the Poisson's ratio and a/W is illustrated in both graphical and tabulated fonns for S/W = 4. Error margins are discussed when Φ is taken as 2.00 universally for all materials exhibiting linear elastic behavior when a/W exceeds 0.5. The Φ value is experimentally detennined for several a/W ratios using a polymeric material. This experimental result is compared with an analytic prediction shown in the present study. The prediction is in good agreement with the experimental result.     

A new method to calculate k1 for semi-elliptical surface cracks in finite plates

Irwin's solution of the stress intensity factor K_I for an embedded elliptical cracks was extended to solve for K_I for semi-elliptical surface cracks in finite plates. A double series was set up to express the displacement of the crack surface, and the unknown coefficients of the series were determined by the crack surface displacements of two dimensional edge cracks and center cracks. The maximum displacement was determined with an energy method. The results reflected the influence of both the relative crack depth a/t and the relative crack length c/W. The cases in which elliptical axis ratio a/c > 1 were also included.     

Effect of fibre angle on fracture properties of unidirectional flyash filled FRP composites

The fracture properties of unidirectional flyash filled and unfilled glass fibre and carbon fibre reinforced epoxy resin composites are studied in relation to the variation of width ratio (a/W) and fibre angle. The results indicate that the fracture toughness, fracture surface energy and change in elastic strain energy are dependent on the width ratio but the effect of fibre angle between 30 and 60° is not very dependent on fracture properties due to the arrest of the crack path in fibre composites by flyash particles.     

Resistance curves for crack growth under plane-stress conditions in an elastic perfectly-plastic material

A recently developed solution for the plastic strain, ε^P_y(x, t), on the crack line is used in conjunction with a critical strain criterion to construct curves for k_R(a) versus a, where a is the increase in crack length. Resistance curves have been computed for various values of the critical plastic strain. They show a monotonic increase of K_R(a) with increase in crack length, to a constant steady-state value.     

Applying strain energy density factor theory to propagation estimating of surface crack in tubular T-joints

The propagation direction of a surface crack in tubular T-joints and the surface crack profile are studied in this paper. By using Photoelasticity and Finite Element method, the distribution of Stress Intensity Factor (SIF) along the front edge of the prefabricated semi-elliptic surface cracks at the hot spots of tubular T-joints is obtained. The results show that the cracks are subjected to mix-mode loading, and the distribution of SIF along the front edge of the crack depends not only on a/T, the ratio of crack depth to the thickness of chord wall, but also largely on shape ratio a/c, the ratio of depth of the crack a to its length c. It can also be predicted that there exists a certain precedent propagation direction for a surface crack with a certain a/c. According to the Strain Energy Density Factor theory the condition of constant strain energy density factor S on the front edge of the crack will be enforced on each point of the prosective crack profile, so that the crack profile can be pre-estimated.     

Effect of loadline shift on applied crack tip stress intensity in WOL specimens

A change in applied stress intensity due to shifting of load line from the pin hole to a wedge located on the outside edge of the notch has been investigated by: (1) finite element analysis, (2) measurements of front face crack opening displacement and (3) strain relaxation near the crack tip.

Results show that this wedge loading procedure will result in a significant drop, up to a factor of two, in applied stress intensity. The drop in stress intensity is inversely related to the crack length (expressed by a/W). This drop in stress intensity is due to overall specimen distortion because of load line shift and local deformation of the wedge and notch surfaces. Implications of this drop on Stress Corrosion Cracking results are discussed. For reliable stress corrosion testing, modifications in specimen geometries and loading procedures are suggested.     

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

Experimental results on mode I and mixed mode stable crack growth under static loadings through an aluminium alloy (D16AT) are presented. The compact tension type of geometry was employed for both the sets of tests. Data pertaining to load-deflection diagrams, crack opening displacements, crack front geometry, etc., are included. There is a greater spurt of crack growth at the initiation stage in a mixed mode than in mode I. The crack opening angle (COA) remained nearly constant during the whole stable growth. There is a substantial tunneling, the extent of which increases as the extension progresses in both mode I and mixed mode. The tunneling reduces as the ratio a₀/W increases. Because of this tunneling, the COD at a point finite distance behind the crack tip and on the specimen surface is much more than expected. At the maximum load the tunneling is 2 to 3.5 mm in the case of mode I. The crack extends initially almost along a straight line at an angle with the initial crack in a mixed mode. The maximum to initiation load ratio varied in the range 1.50 to 1.75 for the whole range of tests.     

Mechanics and mechanisms of delamination in a poly(ether sulphone)—Fibre composite

The interlaminar fracture behaviour of AS4/PES (poly(ether sulphone)) composite has been investigated in Mode I, Mode II and for fixed Mode I to Mode II ratios of 0·84, 1·33 and 2·13. The data obtained from these tests have been analysed using several different analytical approaches. The results obtained show that in Mode I the interlaminar crack growth in double cantilever beam (DCB) specimens is accompanied by fibre bridging behind the crack tip and by splitting at the crack tip, and in Mode II by the formation of a damage zone at the crack tip. These failure mechanisms are shown to increase the value of the interlaminar fracture energy considerably as the crack propagates through the composite, i.e. a rising ‘R-curve’ is measured. It is shown also that the value of the interlaminar fracture energy at crack initiation in Mode I, G_CI (init), increases as the length of the initial precrack is increased. The lowest G_IC (init) value obtained for the poly(ether sulphone) (PES) composite in this study is 0·8 kJm⁻², and this value was ascertained from a specimen with the precrack being grown by about 2 mm ahead of the initial crack (a₀ = 23 mm, a_p = 25 mm). The typical Mode II steady-state propagation energy, G_IIC (s/s-prop), value obtained for the specimens was about 2·0 kJm⁻². The length of the initial precrack had no significant effect on the G_IIC (init) and G_I/IIC (init) values. The Mode II tests gave values of G_IIC (init) = 1·25 kJm⁻² and of G_IIC (s/s-prop) = 1·85 kJm⁻². Finally, the failure loci for the PES composite have been constructed and theoretical expressions to describe these data considered.     

Weight function calculations for mixedmode fracture problems with the virtual crack extension technique

An efficient finite element method is presented for calculating the stress intensity factors (K_I and K_II) and the weight functions for mixed-mode cracks with one virtual crack extension. The computational efficiency is enhanced through the use of singular elements and the application of colinear virtual crack extension (VCE) technique to symmetric mesh in cracktip neighborhood. This symmetric mesh in crack-tip vicinity permits the analytical separation of strain energy release rate into G_I for Mode I and G_II for Mode II for the mixed fracture problems with the colinear virtual crack extension.

Rice's displacement derivative representation of weight function vector for symmetric crack has been extended to the mixed fracture mode at nodal location (x_i,y_i) with crack length (a) and inclination angle (β) as h_I(II)(x_i, y_i, a, β) = (H/2K_I(II)(∂U_I(II)(x_i, y_i, a, β/∂a).

This equation permits explicit determination of weight functions for the entire structure of a given asymmetric crack geometry with colinear VCE technique. The explicit weight functions for mixed fracture mode depend strongly on the constraint conditions. The method of obtaining the required stress intensity factors of a given asymmetric crack geometry, from the weight function concept under the selected constraint conditions, which are different from constraint conditions used in the available weight functions for the same crack geometry, is also presented in this paper. This is accomplished by combining the predetermined explicit weight functions with the self-equilibrium forces at their application locations. These self-equilibrium forces include both the applied surface tractions and the reaction forces induced from the constraint conditions.     

Finite element analysis of an interface crack with large crack-tip contact zones

There is considerable ambiguity regarding the limiting values of the strain energy release rate (SERR) components at the tips of a crack lying along the interface between two dissimilar isotropic media. In this paper this aspect is examined using finite element analysis and Modified Crack Closure Integral (MCCI) for a problem in which the material properties are chosen so as to cause a large size crack-tip contact zone. By careful choice of this problem, interpenetration of the crack faces in the crack-tip contact zones is observed for the first time in the finite element analysis. Earlier solutions primarily on remote mode 1 loading reported that SERR components do not converge as the virtual crack extension Δa → 0 and that these components show an oscillatory nature when Δa is less than the contact zone size r_c. In the present work, multipoint constraints are imposed on crack face normal displacements in the contact zone and meaningful results are generated for both remote tension and shear loading cases. The apparent nonconvergence of the SERR components as Δa → 0 can be explained if these components are considered as functions of Δa, and Δa is considered as the actual crack growth step size.     

Growth mechanism of stress corrosion cracking in high strength steel

Stress corrosion crack growth rates are measured at sveral stress intensity levels for low-tempered 4340 steel in 0.1N H₂SO₄ solution. The characteristics of the growth rates are divided into three regions of stress intensity factors: Region I near K_1SCC; Region III near unstable fracture toughness, K_1SC; and Region II, which lies between the two. K_1SCC is the value of K at which no crack growth can be detected after 240 hr.

In order to explain these experimental results, the crack initiation analysis reported in a previous paper is extended to the growth rates. A detached crack initiates and grows at the tip of an already existing crack. When the detached crack reaches the tip of the main crack, the process repeats as a new existing crack.

A relationship between crack growth rate, v, and stress intensity factor, K, is obtained as a function of b/a and a = b + d, where b is the distance from the tip of the main crack to the detached crack, and d is the ydrogen atom saturated domain.

The experimental data are in good agreement with the theoretical values in Region II when a = 0.02 mm, b/a = 0.8, c₁/c₀ = 2.8 for 200°C tempered specimens and a = 0.015 mm, b/a = 0.7, c₁/c₀ = 3.0, ρ_b = 0.055 mm for 400°C tempered specimens, where ρ_b is a fictitious notch radius. The plateau part in Region II for 400°C tempered specimens is also successfully explained by the present theory. For Region III, the value of b/a will be almost equal to 1 because v → ∞ for b/a → 1. On the other hand, for Region I, b/a will be zero, since the value of v becomes negligibly small and no crack growth is observable.     

Crack growth resistance characterized by the strain energy density function

Stable ductile fracture of a typical metal alloy is found to be governed by the condition dS/da = const., i.e. the rate change of the strain energy density S with crack length 2a (or a) remained constant. Since fracture and/or yielding are load rate dependent, the incremental theory of plasticity is employed for analyzing crack growth where unloading in the material near the crack can take place. Attention is focused on the energy per unit volume, dW/dV, stored along the prospective path of crack growth. The nearest neighbor continuum element must necessarily be at a finite distance r from the crack front. This leads to the general relation dW/dV = S/R. The critical value (dW/dV)_c representing the area under the uniaxial true stress and strain curve is assumed to correspond with failure of material elements. If yielding and unloading occurred locally, a certain amount of irrecoverable energy will not be available for dissipation during macrocracking. Hence, the threshold energy density must be modified to read as (dW/dV)_c^* < (dW/dV)_c. The quantity (dW/dV)_c may be regarded as the crack growth resistance whose magnitude decreases with increasing distance from the crack tip at which point yielding is most intensified.

The results are displayed graphically and shown that the condition dS/da = const. provides a rational means of collating and interpreting ductile fracture data.     

Modelling of ductile fracture initiation in strength mismatched welded joint

In this paper, the effect of strength mismatch and width of the welded joints on the stress–strain distribution in the crack tip region has been discussed. The single-edge notched bend (SENB) specimens (precrack length a₀/W = 0.32) were experimentally and numerically analysed. The model of local approach to fracture, proposed by Gurson, Tvergaard and Needleman, was used. High-strength low-alloyed (HSLA) steel was used as a base metal in quenched and tempered condition. The flux-cored arc-welding process in shielding gas was used. Two different fillers were selected to make over- and undermatched weld metal. The experimental analysis of fracture behaviour of the over- and undermatched welded joints was followed by numerical computations of void volume fraction in front of the crack tip. The critical void volume fraction, f_c, used in prediction of the crack growth initiation on the SENB specimen had been previously determined on a round smooth specimen. Three widths of weld metal were considered: 6, 12 and 18 mm. A comparison of the crack tip opening displacement (CTOD) values corresponding to crack initiation in the SENB specimens is given, as determined both experimentally and using the GTN model.     

Stress evolution during isochronal annealing of Ni/Si system

Nickel films on Si(001) substrates were annealed in vacuum at a ramp rate of 5°C/min. The total force per unit width (F/W) in the film during isochronal annealing was determined using a laser scanning method for substrate curvature measurements. During heat treatment, several abrupt changes of F/W in the film were observed. A clear correlation between the evolution of F/W and the phase formation sequence was found. X-ray diffraction and sheet resistance measurements revealed that these changes of F/W coincide with the formation sequence of Ni₂Si, NiSi, and NiSi₂.     

Determination of the fracture toughness of fabric reinforced composites by the J-integral approach

The fracture behaviour of a glass-fabric-reinforced epoxy composite has been investigated experimentally. Load-displacement curves for single-edge-notched specimens were obtained on an MTS system and the J-integral evaluated through its energy rate interpretation. J_c, the critical value of the J-integral, obtained directly for a₀/w > 0·4 and that obtained through an extrapolation procedure for a₀/w < 0·4 compare quite well. J_c appears to be independent of crack length for specimen widths between 15 and 45 mm. J_c for ±45° specimens is less than half that for 0/90 specimens.     

Exploring the fracture toughness KIE and KIC of a medium-Strength steel plate using the surface-flaw test

The fracture toughness of a 30 CrMnSiA steel plate of three thicknesses (10,8 and 5 mm) and three widths (110,80 and 56 mm) has been investigated by using surface-flaw method under room temperature. It is not easy to compute the value of K_IE by the maximum applied load. But the values of K_IE and K_IC could be obtained easily, if the computation of the conditional applied load P₁₀ and P₅ based on the relative effective extension Δa/a₀ = 10% and 5% were adopted, together with the conditions of P_max/P₁₀ 1.2 and P_max/P₅ 1.3. The K_R — Δ_a curve, i.e. the resistance-curve described by the parameter K, has been plotted. The values of K_IC and K_IE are then the resistances corresponding to the real extensions of flaws of Δ/a₀ = 2 and 7%, respectively. These values so obtained are in good agreement with the computed values of K_IC and K_IE by using the conditional applied loads. The values of K_IC and K_IE so obtained are also in agreement with the value of K_IC converted from the J-integral and the effective value of K_IE computed by the maximum applied load, respectively.

An approximate relation between K_IC and K_IE has been found to be: K_IC = (0.85˜0.95)K_IE.

The requirements for the dimensions of specimens are: Thickness of plate: B 1.0(K_IC/σ_0.2)² or 1.25(K_ICσ_0.2)²]; Width of plate: 8 W/B 10, 4 W/2c 5; Effective length: l 2W.     

Use of double clip gauge method to measure the plastic rotational factor rp

The value of the plastic rotational factor r_p at initiation in 3-point bend specimens with deep and shallow notches has been studied by using the double clip gauge method and it is shown that r_p is decreasing with decreasing of a/W, the experimental results agreeing well with the experimental results by using a clip gauge and catalytically hardening silicone rubber Unitex Xantropren Blue dental impression material.     

Creep crack propagation in austenitic stainless steel at elevated temperatures

Creep crack propagation behavior at high temperature was investigated for type 304 stainless steel. The present experiment reveals that creep crack propagation is explained better in terms of K than in terms of σ_net. The rate of the creep crack propagation is represented by the Arrhenius equation. The activation energy is higher in the present experiment compared with the case of fatigue. Main crack extends by means of joining micro-cracks initiated at vicinity of the main crack tip. Creep rupture is occured when the value of stress intensity factor reaches its critical value which increases with decreasing temperature but independent of stress level. It is found that the creep rupture time is expressed as a function of initial stress and initial crack size, and good agreement is obtained between observed and calculated times to rupture.     

Effects of crack size and weld metal mismatch on the has cleavage toughness of wide plates

The heat affect zone (HAZ) is in many cases considered to be the most critical part of a weldment. In this paper, the effect of crack size and weld metal mismatch on the HAZ cleavage toughness of wide plate specimens with X-groove has been investigated by the J-Q-M theories and a simple micromechanism for cleavage fracture. Two crack sizes have been studied (a/w = 0.1 and 0.3). In the analyses, the HAZ yield strength is assumed to be higher than the base metal. For each crack size, weld metal local overmatch and local evenmatch with respect to the HAZ are considered. For a given global strain, the results indicate that weld metal overmatch and evenmatch yield the same crack tip loading in terms of J-integral for a/w = 0.3. For a/w = 0.1, overmatch gives lower crack tip loading than evenmatch. For a given crack tip loading, weld metal local evenmatch in general results in less effective crack tip loading than the overmatch. Overmatch is detrimental to HAZ toughness, but this detrimental effect becomes less significant when the crack size decreases.