The mode III full-field solution in elastic materials with strain gradient effects

The near-tip asymptotic field and full-field solution are obtained for a mode III crack in an elastic material with strain gradient effects. The asymptotic analysis shows that, even though the near-tip field is governed by a single parameter B (similar to the mode III stress intensity factor), the near-tip field is very different from the classical K_III field; stresses have r ^-3/2 singularity near the crack tip, and are significantly larger than the classical K _III field within a zone of size l to the crack tip, where l is an intrinsic material length, depending on microstructures in the material. This high-order stress singularity, however, does not violate the boundness of strain energy around a crack tip. The parameter B of the near-tip asymptotic field has been determined for two anti-plane shear loadings: the remotely imposed classical K _III field, and the arbitrary shear stress tractions on crack faces. The mode III full-field solution is obtained analytically for an elastic material with strain gradient effects subjected to remotely imposed classical K _III field. It shows that the near-tip asymptotic field dominates within a zone of size 0.5 l to the crack tip, while strain gradient effects are clearly observed within 5l. It is also shown that the conventional way to evaluate the crack tip energy release rate would lead to an incorrect, infinite value. A new evaluation gives a finite crack tip energy release rate, and is identical to the J-integral. This revised version was published online in August 2006 with corrections to the Cover Date.     

Softening and snap-back instability in cohesive solids

The nature of the crack and the structure behaviour can range from ductile to brittle, depending on material properties, structure geometry, loading condition and external constraints. The influence of variation in fracture toughness, tensile strength and geometrical size scale is investigated on the basis of the π-theorem of dimensional analysis. Strength and toughness present in fact different physical dimensions and any consistent fracture criterion must describe energy dissipation per unit of volume and per unit of crack area respectively. A cohesive crack model is proposed aiming at describing the size effects of fracture mechanics, i.e. the transition from ductile to brittle structure behaviour by increasing the size scale and keeping the geometrical shape unchanged. For extremely brittle cases (e.g. initially uncracked specimens, large and/or slender structures, low fracture toughness, high tensile strength, etc.) a snap-back instability in the equilibrium path occurs and the load–deflection softening branch assumes a positive slope. Both load and deflection must decrease to obtain a slow and controlled crack propagation (whereas in normal softening only the load must decrease). If the loading process is deflection-controlled, the loading capacity presents a discontinuity with a negative jump. It is proved that such a catastrophic event tends to reproduce the classical LEFM-instability (K_I = K_IC) for small fracture toughnesses and/or for large structure sizes. In these cases, neither the plastic zone develops nor slow crack growth occurs before unstable crack propagation.     

Effect of specimen size in determining ductile to brittle transition temperature

Ductile to brittle transition temperature (DBTT) for 9Cr–1Mo steel has been determined from Charpy impact testing for full size and subsized specimens. DBTT was obtained at various percentage of upper shelf energy (USE). Assuming that most of the energy is spent in crack initiation, notch root volumes of subsized specimens (V_NS) were normalised with full size specimen (V_NF), and a power law relationship between DBTT and notch root volume has been established. From finite element method, it is observed that the sum of von Mises stress (σ_eq) and hydrostatic stress (σ_h) reaches ～2400 MPa (fracture stress, σ_f*) as the specimen dimension decreases at a temperature corresponding to 33% USE. This corresponds to ～68 J of full size specimen used in the determination of nil ductility transition temperature.     

POP-IN AND CRACK ARREST IN AN HY80 WELD

It is generally thought that, when a material is in its brittle to ductile transition, it is more difficult to design for crack arrest than to prevent crack initiation (cleavage). This report shows that this is not always true for weldments. Comparison is made between compact crack arrest (CCA), K_a, and crack tip opening displacement (CTOD), K_Jc, toughness for the same HY80 weld. The value of K_a is shown to be much higher than the minimum K_Jc for pop-in fracture initiation. It is considered that the results support the conclusion of Japanese research workers (Arimochi and Isaka) that small pop-ins (in the CTOD test) propagate and arrest without load drop. It follows that prediction of structural failure for weldments need not be based on minimum pop-in toughness from CTOD tests.     

A theoretical analysis on the dynamic cleavage cracking in a constant-K specimen

Summary. Through an energy analysis of the cleavage cracking in a constant-K sample, the analytical solution of the dynamic fracture resistance for a brittle, homogeneous material is obtained. The dependence of the crack behavior on the accumulated continuum dissipation associated with the dynamic effect is analyzed. The relationship between the critical energy release rate of crack arrest and the applied stress intensity factor is discussed in detail.     

Fractal effects of crack propagation on dynamic stress intensity factors and crack velocities

Crack extension paths are often irregular, producing rough fracture surfaces which have a fractal geometry. In this paper, crack tip motion along a fractal crack trace is analysed. A fractal kinking model of the crack extension path is established to describe irregular crack growth. A formula is derived to describe the effects of fractal crack propagation on the dynamic stress intensity factor and on crack velocity. The ratio of the dynamic stress intensity factor to the applied stress intensity factor K(L(D, t), V)/K(L(t), 0), is a function of apparent crack velocity V_o, microstructure parameter d/a (grain size/crack increment step length), fractal dimension D, and fractal kinking angle of crack extension path . For fractal crack propagation, the apparent (or measured) crack velocity V_o, cannot approach the Rayleigh wave speed Cr. Why V_o is significantly lower than Cr in dynamic fracture experiments can be explained by the effects of fractal crack propagation. The dynamic stress intensity factor and apparent crack velocity are strongly affected by the microstructure parameter (d/a), fractal dimension D, and fractal kinking angle of crack extension path . This is in good agreement with experimental findings.     

State‐of‐the‐art review on extended stress intensity factor concepts

The stress intensity factor concept for describing the stress field at pointed crack or slit tips is well known from fracture mechanics. It has been substantially extended since Williams' basic contribution (1952) on stress fields at angular corners. One extension refers to pointed V‐notches with stress intensities depending on the notch opening angle. The loading‐mode‐related simple notch stress intensity factors K₁, K₂ and K₃ are introduced. Another extension refers to rounded notches with crack shape or V‐notch shape in two variants: parabolic, elliptic or hyperbolic notches (‘blunt notches’) on the one hand and root hole notches (‘keyholes’ when considering crack shapes) on the other hand. Here, the loading‐mode‐related generalised notch stress intensity factors K_1ρ, K_2ρ and K_3ρ are defined. The concepts of elastic stress intensity factor, notch stress intensity factor and generalised notch stress intensity factor are extended into the range of elastic–plastic (work‐hardening) or perfectly plastic notch tip or notch root behaviour. Here, the plastic notch stress intensity factors K_1p, K_2p and K_3p are of relevance. The elastic notch stress intensity factors are used to describe the fatigue strength of fillet‐welded attachment joints. The fracture toughness of brittle materials may also be evaluated on this basis. The plastic notch stress intensity factors characterise the stress and strain field at pointed V‐notch tips. A new version of the Neuber rule accounting for the influence of the notch opening angle is presented.     

The value of the J-integral at the onset of crack extension from a weld defect: Weld material is softer 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 _w, 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 _w depends on the flow properties of the weld and parent materials, the crack size and the weld thickness.     

Crack growth by grain boundary cavitation in the transient and extensive creep regimes

Crack growth due to cavity growth and coalescence along grain boundaries is analyzed under transient and extensive creep conditions in a compact tension specimen. Account is taken of the finite geometry changes accompanying crack tip blunting. The material is characterized as an elastic-power law creeping solid with an additional contribution to the creep rate arising from a given density of cavitating grain boundary facets. All voids are assumed present from the outset and distributed on a given density of cavitating grain boundary facets. The evolution of the stress fields with crack growth under three load histories is described in some detail for a relatively ductile material. The full-field plane strain finite element calculations show the competing effects of stress relaxation due to constrained creep, diffusion and crack tip blunting, and of stress increase due to the instantaneous elastic response to crack growth. At very high crack growth rates the Hui-Riedel fields dominate the crack tip region. However, the high growth rates are not sustained for any length of time in the compact tension geometry analyzed. The region of dominance of the Hui-Riedel field shrinks rapidly so that the near-tip fields are controlled by the HRR-type field shortly after the onset of crack growth. Crack growth rates under various conditions of loading and spanning the range of times from small scale creep to extensive creep are obtained. We show that there is a strong similarity between crack growth history and the behaviour of the C(t) and C _t parameters, so that crack growth rates correlate rather well with C(t) and C _t .A relatively brittle material is also considered that has a very different near-tip stress field and crack growth history.Visiting Professor, Brown University, August 1988 through December 1989.     

Effects of solidification structure on tear resistance of Al–7% Si–0.4% Mg cast alloys

The tear resistance behaviour of Al–7% Si–0.4% Mg cast alloys was examined using Kahn‐type tear test specimens. Tests were performed for two permanent mould casts with an ordinary dendrite structure and a semi‐liquid die cast with a globular cell and fine grain structure. The microstructure of the two permanent mould casts was controlled by the cooling rates and the addition of Ti elements. Tear resistance was evaluated by the ‘pop‐in’ stress, the energies required for crack initiation, UE_i and the crack propagation, UE_p. Special attention was paid to an effective microstructural parameter for tear resistance improvement. Pop‐in, indicating sudden crack extension and arrest, was observed in all specimens. Homogeneous deformation occurs near the notch tip of the semi‐liquid die cast, characterized by a refined grain structure. Refinement of the grain size is more effective than that of the dendrite cell size or eutectic Si particle size to increase the energy for crack initiation. Unit propagation energy, UE_p, can be converted into a critical stress intensity factor, K_c, which in the semi‐liquid die cast was improved due to an increased amount of slant or shear fracture surface.     

A model of brittle fracture propagation part I—continuum aspects

The micromechanism of crack propagation in steel is described and analyzed in continuum terms and related to the macroscopic fracture behavior. It is proposed that propagation of cleavage microcracks through favorably oriented grains ahead of the main crack tip is the principal weakening mode in brittle fracture. This easy cleavage process proceeds in the Griffith manner and follows a continuous, multiply connected, nearly planar path with a very irregular front which spreads both forward and laterally and leaves behind disconnected links which span the prospective fracture surface. A discrete crack zone which extends over many grains thus exists at the tip of a running brittle crack. Final separation of the links is preceeded by plastic straining within the crack zone and occurs gradually with the increasing crack opening displacement. It is suggested that in low stress fracture, straining of the links is the only deformation mode. However, it is recognized that under certain conditions plastic enclaves may adjoin the crack zone. This deformation mode is associated with high stress fracture, energy transition and eventually with crack arrest.

Energy dissipation resulting from the two deformation mechanisms is related to crack velocity, applied load and temperature and the crack velocity in a given material is expressed as a function of the external conditions. Fracture initiation and crack arrest are then discussed in terms of the conditions which are necessary to maintain the propagation process. Finally, the dimensions of a small scale crack tip zone for a steady state, plane strain crack are evaluated as functions of material properties and the elastic stress intensity factor.

The microstructural aspects of brittle fracture will be discussed in a separate Part 2 [1].     

Plane strain fracture toughness of modern ferritic structural steels

Abstract

The temperature dependence of the plane strain fracture toughness of a low carbon, fine grain, ferritic steel for structural applications is investigated. The ductile–brittle transition is found to occur in the interval between 160 and 184 K. The experimental results are interpreted by an analytical model which permits calculation of the plane strain fracture toughness K _1c in the brittle domain as a function of the tensile properties and the cleavage fracture stress, making use of a piecewise approximation for the distribution of tensile stress on the crack axis and applying a deterministic fracture criterion at the stress peak. A similar criterion, which consists of equating the severest strain on the crack axis to a critical strain for cavity nucleation, provides the upper shelf fracture toughness. A relatively simple figure for predicting the transition temperature of steels in this family as a function of material properties can be obtained in this way.     

On fast fracture in an elastic-(plastic)-viscoplastic solid Part II – The motion of crack

The motion of a crack in an elastic-(plastic )-viscoplastic medium is studied in terms of an energetic analysis. Combined with the stress and velocity fields obtained in Part 1, Kishimoto's energy integral, , is used as a crack driving force to determine its motion. The major results obtained are: (1) dependence of crack speed on a modified near-field parameter, K _I tip, (or equivalently, a modified dynamic energy release, G _I tip), which is different from the usual stress intensity factor K _I of an elastic crack-tip field but is related to it; (2) influence of inelastic effect, such as the viscoplastic exponent n, on the motion of the crack; and (3) stability condition of crack motion. In particular, for the last point, it has been found that, for a given loading and material coefficients, there exist two possible motions of the crack: one is stable crack growth and the other is unstable fracture. The lower and upper bounds of crack motion are also discussed. It is finally shown that the maximum crack velocity is lower than the Rayleigh wave speed, and is dependent on the viscoplastic exponent of the material.     

Some cases of different structural sensitivity of impact strength and fracture toughness

Conclusions Two cases of practical importance are observed of a breakdown in the symbatic correlation of impact strength and fracture toughness concerning the influence of overheating before hardening and also of irreversible temper brittleness of high-strength steels. In both cases the breakdown in the correlation is related to differences in the structural and mechanical situations occurring at the opening of stress concentrators differing in the sharpness of the notch and, consequently, in the dimensions of the zones of plastic deformation and the degree of triaxiality of the stressed and deformed state.Differences in the behavior of K_Ic anda _n with overheating of high-strength low-temperature-tempered steels reflect the fact of a decrease in the work for origin of a brittle crack with an increase in austenitic grain size. In some steels this is the overwhelming portion of the work for failure of Mesnager samples.A necessary condition for the appearance of temper brittleness in fracture-toughness tests is a shift in the temperature range of its appearance of the mechanism of propagation of a crack from intragranular to intergranular.The above-described breakdown in the correlation between impact strength and fracture toughness will appare: be characteristic of other cases of treatment of materials leading to the appearance of appreciable diffère:; s in the strength of layers near the boundary and of the body of the grain with a low level of material plasticity.The cases considered are an indication of the incorrectness of choosing fracture toughness as a universal index of resistance to brittle failure of alloys without taking into consideration their structural state and the specific elastoplastic situation in mechanical tests determining the conditions of formation and growth of a brittle crack.With an increase in tempering temperature and also with a drop in carbon content in the steel there is a decrease in the share of the work for origin of a crack ina _n. In connection with this for high-temperature-tempered and low-carbon steels fracture toughness becomes a more representative characteristic of resistance to brittle failure of alloys and maintains a symbatic correlation with impact strength.Translated from Fiziko-Khimicheskaya Mekhanika Materialov, Vol. 14, No. 6, pp. 64–71, November–December, 1978.     

CORROSION FATIGUE FRACTURE BEHAVIOUR OF A SiC WHISKERALUMINIUM MATRIX COMPOSITE UNDER COMBINED TENSIONTORSION LOADING

We describe an investigation into the fatigue fracture behaviour under combined tension–torsion loading of a SiC whisker-reinforced A6061 aluminium alloy fabricated by a squeeze casting process. Special attention was paid to the environmental effects on fatigue fracture behaviour. Tests were conducted on both the composite and its unreinforced matrix material, A6061-T6, under load-controlled conditions with a constant value of the combined stress ratio, α = τ_max /σ_max in laboratory air or in a 3.5% NaCl solution at the free corrosion potential. The corrosion fatigue strength of both the matrix and composite was less in the solution than in air. The dominating mechanical factor that determined the fatigue strength in air was either the maximum principal stress or the von Mises-type equivalent stress, depending on the combined stress ratio. However, in the 3.5% NaCl solution, the corrosion fatigue strength of both materials was determined by the maximum principal stress, irrespective of the combined stress ratio. In the case of the matrix material, crack initiation occurred by a brittle facet normal to the principal stress due to hydrogen embrittlement. However, in the composite material, the crack was initiated not at the brittle facet, but at a corrosion pit formed on the specimen surface. At the bottom of the pit, a crack normal to the principal stress was nucleated and propagated, resulting in final failure. Pitting corrosion was nucleated at an early stage of fatigue life, i.e. about 1% of total fatigue life. However, crack initiation at the bottom of a pit was close to the terminal stage, i.e. about 70% or more of total fatigue life. The dominating factor which determined crack initiation at a pit was the Mode I stress intensity factor obtained by assuming the pit to be a sharp crack. Initiation and propagation due to pitting corrosion and crack growth were closely examined, and the fatigue fracture mechanisms and influence of the 3.5% NaCl solution on fatigue strength of the composite and matrix under combined tension–torsion loading were examined in detail.     

Fatigue behaviour of friction stir welded AA2024‐T3 alloy: longitudinal and transverse crack growth

The fatigue crack growth properties of friction stir welded joints of 2024‐T3 aluminium alloy have been studied under constant load amplitude (increasing‐ΔK), with special emphasis on the residual stress (inverse weight function) effects on longitudinal and transverse crack growth rate predictions (Glinka's method). In general, welded joints were more resistant to longitudinally growing fatigue cracks than the parent material at threshold ΔK values, when beneficial thermal residual stresses decelerated crack growth rate, while the opposite behaviour was observed next to K_C instability, basically due to monotonic fracture modes intercepting fatigue crack growth in weld microstructures. As a result, fatigue crack growth rate (FCGR) predictions were conservative at lower propagation rates and non‐conservative for faster cracks. Regarding transverse cracks, intense compressive residual stresses rendered welded plates more fatigue resistant than neat parent plate. However, once the crack tip entered the more brittle weld region substantial acceleration of FCGR occurred due to operative monotonic tensile modes of fracture, leading to non‐conservative crack growth rate predictions next to K_C instability. At threshold ΔK values non‐conservative predictions values resulted from residual stress relaxation. Improvements on predicted FCGR values were strongly dependent on how the progressive plastic relaxation of the residual stress field was considered.     

Positron lifetime spectroscopy characterization of thermal history effects on polycarbonate

The effect of a short-term anneal aboveT _g on the free volume cavity size and concentration and on the fracture toughness of polycarbonate is examined. The positron annihilation lifetime (PAL) technique is used to measure the change in free volume concentration and cavity size during isothermal relaxation experiments at 10, 20 and 30 ° C. An activation energy of 16.5 kJ mol^–1 is calculated for the relaxation of the annealed polycarbonate, compared to 12.3 kJ mol^–1 for the unannealed material. The fracture toughness and brittle fracture morphology of compact tension specimens are unchanged by the anneal. The similarity in the PAL parameters and physical properties between the unannealed polycarbonate and the material annealed aboveT _g suggests that the short-term anneal does not appreciably alter the structural state of glassy polycarbonate.     

Effect of skin fracture on failure of a bilayer polymer structure

A thin skin of low tensile failure strain, if bonded to the tensile surface of an un-notched impact bend specimen of much tougher material, can change the global failure mode from ductile to brittle. A novel model of this well-known effect is developed and applied to results from impact tests on a tough core of polyamide-polyethylene blend, with a single skin of brittle EVOH. At a fixed crosshead speed, notched specimens of the blend become brittle at a relatively low temperature T _bt. Un-notched bilayer specimens continue to show skin fracture up to a considerably higher temperature T _fs; above this temperature they do not fail at all but below T _bt they too fail in a brittle manner. Within the temperature range from T _fs down to T _bt there is a transition from crack arrest, either at the skin/core interface or further into the core where a crack would not normally propagate, to brittle fracture. This brittle fracture temperature is predicted by modelling the process as a three-phase impact event. In the first phase, the striker bends the bilayer quasi-statically. The second phase begins with instantaneous fracture of the skin at its failure strain. The skin ends retract at finite speed, and a craze grows in the adjacent core material to accommodate the local strain singularity. The last phase is a striker-driven impact event similar to that in a notched bend specimen of the core material, except that the crack-tip craze already bears the adiabatic temperature distribution generated while it was driven open by skin retraction. The criterion for craze decohesion, and hence for a crack jump, is the same adiabatic decohesion criterion which accounts for the speed-dependence of impact fracture in notched monolayer specimens. Applied computationally, this model predicts whether a bilayer structure fails in a brittle way or whether cracks initiated in the skin are arrested, either temporarily or permanently, at the skin/core interface.     

MIXED-MODE FRACTURE MECHANISMS NEAR THE FATIGUE THRESHOLD OF AISI 316 STAINLESS STEEL

Abstract— Near threshold, mixed mode (I and II), fatigue crack growth occurs mainly by two mechanisms, coplanar (or shear) mode and branch (or tensile) mode. For a constant ratio of ΔK_I/ΔK_II the shear mode growth shows a self-arrest character and it would only start again when ΔK_I and ΔK_II are increased. Both shear crack growth and the early stages of tensile crack growth, are of a crystallographic nature; the fatigue crack proceeds along slip planes or grain boundaries. The appearance of the fracture surfaces suggest that the mechanism of crack extension is by developing slip band microcracks which join up to form a macrocrack. This process is thought to be assisted by the nature of the plastic deformation within the reversed plastic zone where high back stresses are set up by dislocation pile-ups against grain boundaries. The interaction of the crack tip stress field with that of the dislocation pile-ups leads to the formation of slip band microcracks and subsequent crack extension. The change from shear mode to tensile mode growth probably occurs when the maximum tensile stress and the microcrack density in the maximum tensile plane direction attain critical values.