Plastic mismatch effect on plasticity induced crack closure: Fatigue crack propagation perpendicularly across a plastically mismatched interface

In the present work, comprehensive investigation of both theoretical analysis and numerical simulation was carried out to investigate the plastic mismatch effect on plasticity induced crack closure (PICC) behavior and effective fatigue crack tip driving force. During the process of crack tip approaching interface, crack tip load and crack tip load ratio will change, resulting in the change of PICC degree. When the crack propagates towards higher strength side, K_op/K_max increases; when the crack propagates towards lower strength side, K_op/K_max decreases firstly and then increases. The two mechanisms of “interface plastic mismatch effect on nominal fatigue crack tip driving force” and “interface plastic mismatch effect on PICC degree” were compared. The second mechanism must be considered when building crack tip driving force model for describing fatigue crack crossing plastically mismatched interface, because it is more physically factual and maybe more important than the first mechanism.     

Effects of microstructure on mixed-mode, high-cycle fatigue crack-growth thresholds in Ti-6Al-4V alloy

Effect of microstructure on mixed‐mode (mode I + II), high‐cycle fatigue thresholds in a Ti‐6Al‐4V alloy is reported over a range of crack sizes from tens of micrometers to in excess of several millimeters. Specifically, two microstructural conditions were examined—a fine‐grained equiaxed bimodal structure (grain size ～20 µm) and a coarser lamellar structure (colony size ～500 µm). Studies were conducted over a range of mode‐mixities, from pure mode I (ΔK_II/ΔK_I = 0) to nearly pure mode II (ΔK_II/ΔK_I ～ 7.1), at load ratios (minimum load/maximum load) between 0.1 and 0.8, with thresholds characterized in terms of the strain‐energy release rate (ΔG) incorporating both tensile and shear‐loading components. In the presence of through‐thickness cracks—large (> 4 mm) compared to microstructural dimensions—significant effects of mode‐mixity and load ratio were observed for both microstructures, with the lamellar alloy generally displaying the better resistance. However, these effects were substantially reduced if allowance was made for crack‐tip shielding. Additionally, when thresholds were measured in the presence of cracks comparable to microstructural dimensions, specifically short (～200 µm) through‐thickness cracks and microstructurally small (< 50 µm) surface cracks, where the influence of crack‐tip shielding would be minimal, such effects were similarly markedly reduced. Moreover, small‐crack ΔG_TH thresholds were some 50–90 times smaller than corresponding large crack values. Such effects are discussed in terms of the dominant role of mode I behaviour and the effects of microstructure (in relation to crack size) in promoting crack‐tip shielding that arises from significant changes in the crack path in the two structures.     

Internal stress behavior of the short ceramic fiber reinforced aluminum alloy under tensile deformation

The in situ measurement of phase stress under tensile deformation on an A6061 alloy reinforced with SiC whiskers (Al/SiCw MMC: Metal Matrix Composite) was performed using the X-ray diffraction technique. In order to raise a preciseness of measurements, we applied a profile fitting technique to separate the nearby located diffraction peak. Tensile deformation on elastic to plastic range was applied by four points bending device and discussed internal stress behavior in the short ceramic fiber reinforced MMC. Phase stress in Al matrix was increased linearly up to 2800×10⁻⁶ in strain and then saturated immediately. On the other hand phase stress in SiC whiskers shows an unstable stress behavior. It was decreased at first because of the Poisson's effect from Al matrix but reversed over 500×10⁻⁶ applied strain. The measured phase stress behavior in elastic region agreed with the calculations using micromechanics based on Eshelby/Mori–Tanaka model except for this unstable internal stress region. The macro stress behavior in plastic region was extremely small than that of the tensile test results. It supposed that the mechanism of strength is not so much the fiber reinforcing as the dispersion strengthening like the Orowan mechanism. Regarding the fatigue property, ΔK_th of the Al/SiC MMC, this was lower than that of the A6061 alloy. On the Al/SiCw MMC specimen, many micro void formations were observed around the fatigue crack tip even under the ΔK_th of A6061. It was considered that these were caused by the high gradient of residual stress on composite process and the unstable stress behavior in low ΔK region.     

Development of ternary Mg based alloy for soldering of AZ31B magnesium alloy

Abstract

Two kinds of ternary Mg based alloys were designed to join the AZ31B magnesium alloy plates by high frequency induction soldering with argon shielding gas. The microstructures and properties of the filler metals and joints were investigated by SEM, X-ray diffraction, differential scanning calorimetry, spreading test and tensile test. The results have shown that the microstructures of Mg–31·5Al–10Sn filler metal mainly consist of Mg₁₇Al₁₂, Mg₂Sn and a trace amount of α-Mg phases, while the microstructures of Mg–29·5Zn–1Sn filler metal include α-Mg phase and Mg₇Zn₃ with a trace of α-Mg and Mg₂Sn phases. Both of the filler metals have narrow melting zones; however, the spreading area of the Mg–31·5Al–10Sn filler metal is much larger than that of the Mg–29·5Zn–1Sn filler metal on the AZ31B base metal. The average tensile strength of solder joints with Mg–31·5Al–10Sn filler metal is a little higher than that of the latter solder joints with Mg–29·5Zn–1Sn filler metal.     

Study on cleavage fracture criteria of the quasi-brittle and micro-inhomogeneous materials

On the bases of recent achievements on the micro-mechanism of cleavage this paper analyses the inherent deficiencies of the stress intensity factor K _I which is used to evaluate the fracture toughness of quasi-brittle and micro-inhomogeneous materials. The K _I parameter can uniquely determine the field intensity ahead of a crack tip in the condition of elastic and small scale yielding (SSY). However, the K _I cannot uniquely determine the critical condition triggering the cleavage fracture in a quasi-brittle and inhomogeneous steel where the cleavage fracture process is not a direct extension of the precrack but is initiated at a variable distance from the precrack tip. The variable distances of cleavage initiations invoke varied critical values of K _I. On the bases of authors' experiments, this paper analyses the physical meaning of the local fracture stress _f, its stability and the feasibility to be used as an engineering parameter for assessing the fracture toughness.     

Ductile–brittle fatigue and fracture behaviour of aluminium/PMMA bimaterial 3PB specimens

Fracture toughness and fatigue crack growth tests and numerical simulations on 3PB specimens were carried out to study the behaviour of a crack lying perpendicular to the interface in a ductile/brittle bimaterial. Polymethylmethacrylate acrylic (PMMA) and aluminium alloy 2024 T531 were joined together using epoxy resin. A precrack was introduced into the ductile material and tests were carried out to obtain fracture toughness and fatigue properties. The body force method and elastic–plastic finite-element analyses were used to simulate the experimental stress intensity K_I and cracking behaviour under monotonic and cyclic loads. It was found that the bimaterial fatigue crack growth rate is higher than that for monolithic aluminium 2024 but lower than the rate for a monolithic PMMA. This agreed with the trend for the fracture toughness values and was consistent with the numerical method results. The initial Mode I stable ductile cracking in the aluminium appears to ‘jump’ the interface and continues under mixed fracture Mode (I and II) in the PMMA material up to the final failure. A consistency between the simulation methods has indicated that the bimaterial fatigue crack growth is dominantly elastic with a small plastic zone near the crack tip.     

Mixed-mode fatigue crack growth behaviour in aluminium alloy

Fatigue crack propagation tests in compact mixed-mode specimens were carried out for several stress intensity ratios of mode I and mode II, K_I/K_II, in AlMgSi1-T6 aluminium alloy with 3 mm thickness. The tests were performed in a standard servo-hydraulic machine. A linkage system was developed in order to permit the variation of the K_I/K_II ratio by changing the loading angle. Crack closure loads were obtained through the compliance technique. A finite element analysis was also done in order to obtain the K_I and K_II values for the different loading angles. Crack closure increases under mixed-mode loading conditions in comparison to mode-I loading due the friction between the crack tip surfaces. Moreover, the crack closure level increases with the K_I/K_II ratio decrease. Correlations of the equivalent values of the effective stress intensity factor with the crack growth rates are also performed. Finally, an elastic–plastic finite element analysis was performed to obtain the plastic zones sizes and shapes and model the effect of mixed-mode loading on crack closure.     

Fracture toughness measurement with fatigue-precracked single edge-notched beam specimens of WC-Co hard metal

The plain-strain fracture toughness of WC-8%Co hard metal, K _IC, was measured using single edge-notched beam (SENB) specimens with fatigue precrack. The fatigue precrack was introduced with compressive fatigue cycling in four-point bending at room temperature. Since stable fatigue-crack propagation was obtained from the notch tip, it was easy to control the fatigue-precrack length. A reasonable K _IC value of 13.3 MPa m^1/2 was obtained with the fatigue-precracked SENB specimens in four-point bending. The compressive fatigue-precracking technique in four-point bending was simple and convenient, and is therefore applicable to precracking in a variety of brittle materials prior to fracture-toughness measurements.     

A computational model and experimental validation of shielding and amplifying effects at a crack tip near perpendicular strength-mismatched interfaces

The stress field around the crack tip near an elastically matched but strength-mismatched interface body in a bimetallic system is influenced when the crack tip yield or cohesive zone spreads to the interface body. The concept of crack tip stress intensity parameter, K _tip, is therefore employed in fracture analysis of the bimetallic body. A computational model to determine K _tip is reviewed in this paper. The model, based upon i) Westergaard??s complex potentials coupled with Kolosov?CMuskhelishvili??s relations between a crack tip stress field and complex potentials and ii) Dugdale??s representation of the cohesive zone clearly indicates shielding or amplifying effects of strength mismatch across the interface, depending upon the direction of the strength gradient, over the crack tip. The model is successfully validated by conducting series of high cycle fatigue tests over Mode I cracks advancing towards various strength-mismatched interfaces in bimetallic compact tension specimens prepared by electron beam welding of elastically identical weak ASTM 4340 alloy and strong MDN 250 maraging steels.     

The influence of elastic mismatch on the size of the plastic zone of a crack terminating at a brittle-ductile interface

This paper presents the results of an investigation of the effects of elastic mismatch on the size of the plastic zone at the tip of cracks terminating at a bimaterial interface. Using the Williams technique, an asymptotic solution is obtained for the magnitude of the crack tip stress singularity and for the stress field associated with a semi-infinite crack impinging on an interface. This solution, together with the Von Mises yield criterion, is used to estimate the location of the plastic zone boundary r ₀ for various levels of the elastic mismatch, which are expressed in terms of the Dundurs constants. Results are expressed in terms of the non-dimensional quantity% MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGak0Jf9crFfpeea0xh9v8qiW7rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOCamaaBa% aaleaacaaIWaaabeaakmaadmaabaWaaSaaaeaacaaIXaaabaWaaOaa% aeaacaaIYaGaeqiWdahaleqaaaaakmaalaaabaGaam4AamaaBaaale% aacaqGjbaabeaaaOqaaiabeo8aZnaaBaaaleaacaaIWaaabeaaaaaa% kiaawUfacaGLDbaadaahaaWcbeqaaiabgkHiTiaaigdacaGGVaGaeq% 4UdWgaaaaa!4832!\[r_0 \left[ {\frac{1}{{\sqrt {2\pi } }}\frac{{k_{\text{I}} }}{{\sigma _0 }}} \right]^{ - 1/\lambda }\]where k _i is the stress intensity factor and ₀ is the yield stress. These results, together with an integral equation solution for k _i , are used to calculate the size of the plastic zone of a crack of length 2a loaded by uniform pressure. It is shown that the location of the boundary of the plastic zone depends strongly on the elastic mismatch.     

COMPARISON OF PLASTIC WORK OF FATIGUE CRACK PROPAGATION IN LOW CARBON STEEL MEASURED BY STRAIN-GAGES AND ELECTRON CHANNELING

Abstract— The plastic work to propagate a fatigue crack by a unit area, U, measured by the foil strain gage technique requires an extrapolation to estimate the contribution closer than 100 μm to the crack tip. This is due to the size of the strain-gages used, 200 × 210 μm. Conversely, the electron channeling technique for determining U is useful mainly close to the crack tip where subgrains form. In the present work U was measured by both techniques in the same low carbon steel at ΔK= 8 MN/m^3/2. The contribution to U from closer than 100 μm of the crack tip was determined to be 1·7 × 10⁶ J/m² using electron channeling and 2·0 × 10⁶ J/m² by extrapolation. The measured contribution to U from further than 100 μm from the crack tip was 3·6 × 10⁶ J/m² giving 5·3 × 10⁶ J/m² for U. Thus, a large amount of energy is absorbed outside the region where sub-grains form. The non-hysteretic plastic work was found to be about four orders of magnitude smaller than the hysteretic plastic work, and may be neglected. A map of the plastic zone results from the strain-gage measurement. Rice's theory predicts the measured plastic zone sizeif the proper material's strength is employed in the formula.     

Ductile crack growth and constraint in pipelines subject to combined loadings

An important failure mode of offshore pipelines is ductile fracture of the pipe wall triggered by a hypothetical welding defect. In this study, pipelines having an external part-through semi-circumferential crack of various sizes, subject to combined internal pressure and inelastic bending are considered. This is done to assess the response of pipelines during both their installation and operational conditions. Detailed 3D nonlinear finite element (FE) models of pipelines are developed. A row of elements ahead of the initial crack front are modeled using a voided plasticity material model, which enables simulation of crack growth and the subsequent fracture failure mode (denoted by the critical curvature, κ_crit). After discussing the typical response characteristics of such pipelines, the FE model is used to parametrically investigate the influence of varying pipe and crack dimensions, and also the internal pressure levels, on κ_crit. In the second part of this paper, the crack tip constraint ahead of a growing crack in such pipes is evaluated and systematically compared to the crack tip constraint of both the traditionally used deeply cracked Single Edge Notch Bend (SENB) specimens and the constraint-matched Single Edge Notch Tensile (SENT) specimens. This is achieved by comparing the crack resistance curves (R-curves) along with stress triaxiality and equivalent plastic strain fields evaluated ahead of a growing crack of the three systems. The results present grounds for justification of usage of SENT specimens in fracture assessment of such pipes as an alternative to the traditional overly conservative SENB specimens.     

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.     

Crack sharpness effects in fracture testing of polymers

Tests on five polymers are described in which the fracture toughness,K _b, was determined in three-point bending using cracks with a range of tip radii. The variation ofK _b with tip radius is modelled using a two criterion elastic model, a stress and a length, and using these it is possible to estimate the sharp crack values and the effects of blunting arising from the plastic zone. A suggestion for a possible standard test is given.     

Division of character zones and elements distribution of Fe3Al/Cr–Ni alloy fusion bonded joint

Abstract

A Fe₃Al/Cr–Ni alloy fusion bonded joint was divided into four character zones of a homogeneous mixture zone, a partial mixture zone, a partially fused zone and a heat affected zone. The microstructures, elements distribution and phase constitutions of the various character zones were analysed via metalloscope, SEM, electron probe microanalysis and X-ray diffraction. The results indicated that the microstructures were dissimilar in the different character zones. A 0·04–0·05 mm austenite rich band existed in the partial mixture zone. The diffusion of Fe, Al, Cr, Ni and C mainly occurred in fusion zone where Cr and Ni diffused into Fe₃Al to substitute some Fe on α ₁, α ₂, and β sublattices to form substitutional solid solution. The phase constitutions of Fe₃Al/Cr–Ni joint were Fe₃Al, γ-Fe, FeAl, NiAl, an unidentified Fe–C compound and an Fe–Cr–C compound (Cr₉Fe)₇C₃.     

Fatigue crack propagation in Al–Sn bearing alloys

Abstract

Fatigue crack propagation has been studied in a series of Al–Sn bearing alloys as a function of microstructure and environment at stress intensity ratios R of 0·7 and 0·1. Fatigue thresholds of tin containing alloys increased with a reduction in content and in continuity of the tin phase in laboratory air. This is interpreted in terms of crack closure, crack growth along the Al/Sn interface, and crack tip blunting mechanisms. Mechanisms that retard fatigue crack growth through the aluminium phase (e.g. by an increase in the reversibility of slip or by an increase in the size of the reverse plastic zone) were found to increase fatigue thresholds. When tested in dry air, the Al/Sn interface shows reduced embrittlement. The consequence of this for fatigue thresholds is complex: at R=0·7, fatigue thresholds increase with a decrease in tin content, while the thresholds are constant at R=0·1.

MST/927     

Effect of notching speed on dynamic fatigue behaviour of polyethylene terephthalate polymers

The influence of notching speed on the fatigue behaviour of crystalline and amorphous polyethylene terephthalate (PET) was investigated. A clear precrack adjacent to the notch tip was found after each crystalline sample was notched, and the precrack length increased when the samples were notched at higher speeds. The failure time, t _f, decreased significantly for samples with longer precrack lengths, and the decrease in t _f due to faster notching speeds was significantly lower for samples of high average molecule weight and calculated tie-molecule density. In contrast, a heart-shaped damaged structure surrounding the notch tip was observed after each amorphous sample was notched, and the size of the damaged zone, adjacent to the notch tip, increased significantly with the notching speed. Furthermore, the time to failure of each amorphous sample increased significantly as the notching speed increased. In fact, most of the increase in t _f is due to an increase in the initiation period, t _i. This significant increase in t _i is attributed to the larger damaged zone caused by higher notching speeds.     

FATIGUE CRACK GROWTH BEHAVIOUR AND FRACTURE RESISTANCE IN CERAMICS

Fatigue crack growth and the fracture resistance curve (R-curve) were investigated in a polycrystalline alumina (AD90) and a silicon carbide whisker-reinforced alumina composite (Al₂O₃-SiC_w) at room temperature in air using a combined loading technique for stabilizing crack growth, and a surface film technique for monitoring crack length. Fatigue crack growth was evaluated successfully with those experimental techniques. Load shedding tests were performed until the crack became dormant, in order to determine the threshold stress intensity factor K_th. Subsequently, the specimens were used for quasi-static crack growth tests under a monotonic loading condition. The R-curves were determined in this experiment; however, fracture resistance did not increase markedly with crack growth. Detailed observations of the crack growth behaviour revealed that the flat R-curve was attributed to the shielding effect of the fatigue crack tip wake. Thus, the fatigue precrack introduced by the load shedding test was not regarded as an ideal crack for determining the R-curve. Fractographic observations were performed to investigate the mechanistic difference between fatigue and quasi-static crack growth. It was found that the cyclic loading produced fretting damage in the wake region and it reduced the shielding effect of the fatigue cracks. Based on the experimental results, the relationship between the fatigue crack growth and the R-curve is discussed as is the significance of K_th as a material parameter.     

Effect of texture evolution on tensile properties of Al–Ni eutectic alloy fabricated by equal channel angular pressing

Abstract

The present study investigated in detail the effect of texture evolution on the mechanical properties of an Al–5·7 wt-%Ni eutectic alloy, which was subjected to severe plastic deformation by the equal channel angular pressing (ECAP) technique. The ECAP procedure was carried out using two strain introduction methods, route B_C and route A, at a temperature of 298 K and a pressing rate of 0·33 mm s^?1. The as pressed microstructures were observed by scanning electron microscopy (SEM) and transmission electron microscopy (TEM). Results indicated that the Al–Ni eutectic alloy specimens after ECAP processing by route B_C and route A methods had very different microstructures, which strongly affected the tensile properties of the specimens. It was demonstrated that after ECAP processing by route B_C, fine Al₃Ni particles of ～300 nm were homogeneously dispersed in the aluminium matrix, and the specimens showed no clear anisotropy in tensile properties. After ECAP processing by route A, however, eutectic textures containing α-Al and Al₃Ni fibrous dispersoids had a highly anisotropic distribution and were demonstrated to have significantly anisotropic tensile properties. Based on the experimental results, the fracture mechanism during tensile testing of the Al–Ni eutectic alloy using different strain induction methods is discussed.     

Fracture of single crystal MgAl2O4

The fracture of single crystal, stoichiometric MgAl₂O₄ spinel, was investigated for the (1 0 0), (1 1 0), and (1 1 1) from room temperature to 1500° C. Two regions of fracture behaviour were observed; a low temperature elastic region where K _lc decreased with increasing temperature, and an elevated temperature region where K _lc increased rapidly with increasing temperature. The elastic region is explained primarily by the decrease of elastic modulus with increasing temperature, whereas the rapid increase of K _lc at elevated temperature is attributed to plastic flow in the vicinity of the crack tip