Complete shear localisation in a steep stress gradient is likely to be more prevalent for tests under strain control. Within the context of the smallstrain flow theory of plasticity, the total. Finite element simulations are performed within a mode i, plane strain modified boundary layer framework by prescribing the two term kt elastic crack tip field as remote boundary. Incorporating this feature produces additional strain rate sensitivity in the constitutive response. Sciencedirect experimental study of strain rate sensitivity to. Negative strain rate sensitivity srs and discontinuous yielding were evidenced, in relation with a drop in fracture toughness. Finite element analysis on crack tip deformation behavior. In such cases, the stress field near the crack tip has sufficient time for. It seems that, although both ratchetting strain and accumulated inelastic strain correlate with the crack growth rates obtained under fatigue and. The stress and plastic strain fields prevailing near a. The thermoelectromechanical jintegral and the thermal.
Crack tip effective strain rates in rate sensitive materials. Evaluating and modeling rate sensitivity in advanced reactor. The latter were used, in combination with the materials cyclic and monotonic. Aalborg universitet crack tip parameters for growing cracks. Mechanical behavior and crack tip plasticity of a strain aging sensitive steel. In some applications, thin copper wires commonly 44 awg bonded to the test structure are used to provide a lowcost method of detecting crack initiation or propagation. Crack tip strain rate models for environmentallyassisted fatigue. Today, it is the critical stress intensity factor k ic, found in the plane strain condition, which is accepted as the defining property in linear elastic fracture mechanics.
The strain rate sensitivity increases beyond 1s 1, up to a value of about 10 3 s 1. A similar expression may be arrived at from irwins crack tip stress rate equation 6. Plane strain crack tip stress and strain fields are presented for materials exhibiting pressure sensitive yielding and plastic volumetric deformation. Thus, the objective of this work is to examine the general structure of these distributions and the plastic zone shapes in a ratesensitive fcc single crystal. Pdf crack tip effective strain rates in rate sensitive. The sharper the crack tip, the larger the stress at the crack tip. Quasistatic crack tip fields in ratesensitive fcc single crystals.
Note the radial stress discontinuity in planestress fullyyielded asymptotic crack tip fields in 12,20. Default model parameters and an equation for the distance from the crack tip at which strain rate is estimated were successful in simplifying the application of the models. Figure 7 shows the strain rate sensitivity of az31b at 200 c for the low strain rate range 0. The present study examines the strainrate sensitivity of four high strength, hightoughness alloys at strain rates ranging from 0. Oct 14, 2007 rate dependence of crack tip processes predicts twinning trends in f. By assuming a creep process zone at a crack vicinity, the material starts to experience creep damage when it enters the process zone at r r c, at the time t0, and accumulates creep strain. The flow stress increases as the strain rate increases.
Pdf crack tip strain rate equation with applications to crack tip. Materials free fulltext analysis and characterization. This paper demonstrates the feasibility of using theoreticallymotivated crack tip strain rate ctsr models to estimate environmentallyassisted. The data reveal that extremely high strain rates or loads are necessary for twin nucleation in al, pt and au, whereas crack tip twinning would regularly occur under typical experimental conditions. Beyond 10 3 s 1 the sensitivity to strain rate becomes extreme. Strain rate sensitivity in superelasticity request pdf.
Parkins 1 department of metallurgy and engineering materials, university of newcastle upon tyne, newcastle upon tyne ne1. Thresholds and growth rates depend on loading rate, and appear most environment sensitive at intermediate crack tip strain rates. The characteristic equation which describes the superplastic behavior is usually written as 1 k b 6 k 4. Dong and pan 21 carried out an elasticplastic analysis of cracks under plane strain and smallscale yielding.
Effects of material rate sensitivity and void nucleation on. In this work, the effects of loading rate, material rate sensitivity and constraint level on quasistatic crack tip fields in a fcc single crystal are studied. Strain rate sensitivity of glass fibreepoxy composite at. Learn vocabulary, terms, and more with flashcards, games, and other study tools. Under the assumption that the artificial viscosity coefficient at the propagating crack tip is in inverse proportion to power law of the plastic strain rate, a rate sensitive constitutive relationship is derived for perfect elasticplastic material. For polymers this rate sensitivity is strong and of great importance when the material. Abstract t he asymptotic stress and strain fields near the tip of a crack which propagates dynamically in a ratesensitive solid are obtained under antiplane shear and plane strain conditions. When the crack tip strain rate is below 104 s1, the crack propagation rate is below 0. In the range of high strain rates, the mechanical behavior of a material is characterized by an increased in strain rate sensitivity. Aermet 100, a modified 4340, modified hp9420, and a recently developed eglin afb steel alloy, es1c. Mesh size sensitivity analysis for interlaminar fracture of. The model is also exper imentally verified by predicting the failure strength of dionysuspentelicon marble over strain rates ranging from. The yield criterion is described by a linear combination of the effective stress and the hydrostatic stress, and the plastic.
Possible crack velocities must lie on intersections of the. Effect of strain rate and temperature on yielding and fracture. Crack tip strain rate an overview sciencedirect topics. Furthermore, for a certain range of the material parameter which characterizes the rate sensitivity of the material, the elastic strain rates near the propagating crack tip are shown to have the same asymptotic radial dependence near the propagating crack tip as the inelastic strain rates. Under the assumption that the artificial viscosity coefficient at the propagating crack tip is in inverse proportion to power law of the plastic strain rate, a ratesensitive constitutive relationship is derived for perfect elasticplastic material. Moreover, a characteristic velocity, at which the toughness becomes independent of the rate sensitivity, has been observed. During oxidation the measured crack length would gradually decrease, until the oxide ruptured, abruptly. Strain rates at the elastoplastic boundary ahead of the notch tip were. The dynamic toughness may also be dependent on crack speed for materials which are strain rate sensitive i1. The crack length and the temperature at the crack tip are measured using an infrared thermography ir camera. Moreover, in the low strain rate regime, the measured flow stress and rvalues are mildly strain rate sensitive at room temperature 81, while as the temperature increases, strong strain rate sensitivity is observed. Neartip strain ratchetting and crack growth at elevated. Crack tip effective strain rates in rate sensitive. So, the overstress is the difference between the upper yield stress and this microscopic yield stress 6.
Li and pan 18 studied the mode i asymptotic, crack tip. Crack tip fields and mechanisms of fracture in ductile. In addition to inertia and strain rate sensitivity. Mechanical behavior and crack tip plasticity of a strain. The problem is formulated within the context of a smallstrain theory for a solid whose mechanical behavior under high strain rates is described by an elasticviscoplastic constitutive relation. Strain rate sensitivity an overview sciencedirect topics. Crack propagation occurs as a result of the release of stored elastic strain energy, but during crack extension kinetic energy is produced that may contribute to crack propagation. It is also clear that the tearing energy is shared evenly when the crack tip is split into two paths of equal length, but as one crack accelerates ahead it quickly increases in tearing energy and leaves the slower crack. The role of crack tip strain rate in the stress corrosion cracking of. The effect of crack tip strain rate and potential on the. This means that the engineering strength will depend on the strain rate or on the duration of the load. Elasticplastic anaiysis of cracks in pressuresensitive materials 1115. Under load control, an initial crack could accelerate. Throughout, emphasis is on the toughness rate sensitivity, as a recent numerical study of a conventional material no gradient effects has indicated a signi cant in uence of both strain rate hardening and crack tip velocity.
In theory the stress at the crack tip where the radius is nearly zero, would tend to infinity. Figure 8 presents the variations of the critical crack mouth opening. Data from lowamplitude dynamic tests agreed well with ei trends from ct and tensile tests. On the other hand, there has been no investigation on the effect of strain rate sensitivity and loading rate on the stress and plastic slip distribution. Fracture analysis in the conventional theory of mechanism. T elastic crack tip field as remote boundary conditions. Up to a strain rate of about 1s 1 only a small to moderate increase in yield strength of about 70mpa for this steel type is obtained. The former is the case for high ductility and strain rate sensitive materials such as lowcarbon steels while the latter has been reported for some fcc materials such as aluminum alloys 2e5. Loading rates and tensile properties fracture toughness twi.
Results on the influence of crack tip plasticity during. Strain rate effects in stress corrosion cracking r. Smallscale yield model for restricted crack tip plastic deformation. The elasticviscoplastic field at the tip of mode ii quasi. Crack tip strain rate models for environmentallyassisted. Crack tip opening displacement how is crack tip opening. Both ratchetting strain and accumulated inelastic strain near the crack tip were utilised in the prediction of the crack growth rates collected in vacuum. Pdf analytical equations for crack tip strain rate are needed for. Walley2 the high strain rate dependence of the flow stress of metals and alloys is described from a dislocation mechanics viewpoint over a range beginning from conventional tensioncompression. To this end, the effects of loading rate, material inertia and strain rate sensitivity on crack tip fields and their influence on fracture mechanisms in fcc single crystals are examined in this work by performing finite element analysis. Loading is assumed to occur at two very different rates which correspond to the quasistatic and high rate tests of couque et al.
It is possible that the crack tip was shortcircuited by a process of repeated oxide formation and rupture. Creep crack growth properties of p91 parent and welded steel. Investigation of crack tip stress and strain fields at crack initiation. Correlation of the high and very high cycle fatigue. A micromechanics based constitutive model for brittle. The strain rate at some point within the material measures the rate at which the distances of adjacent parcels of the material change with time in the neighborhood of that point. Introduction most of the engineering materials suffer from rate sensitivity. Stability, validity, and sensitivity to input parameters of. Ei, total energy to breakage and maximum stress rose with increasing strain rate from 0. The kubinestrinmccormick kemc constitutive law, well suited for this kind of material response, was identified so as to model the mechanical behavior of. High strain rate properties of metals and alloys r. Also, the influence of material strain rate sensitivity on the development of crack tip plastic deformations, and the implications for cleavage propagation and arrest in a material that can undergo a fracture mechanism transition is considered.
Strain gradient plasticity modeling of hydrogen diffusion to the crack tip e. This law is sensitive to both the crack tip stress field and its time derivative. The results on the corresponding planestress crack tip fields are. This overstress can be approximately estimated to 150mpa at 20 c see fig. Crack tip deformation behavior of single crystal superalloy under modeii shear stress condition was evaluated by crystal plasticity finite element method by applying eshelbys inclusion theory to express the relation between microscopic and macroscopic stressstrain character, and the influence of. The role of crack tip strain rate in the stress corrosion cracking of high strength. However, the tdrx is not utterly proportional to the temperature. Strain rate is the change in strain deformation of a material with respect to time the strain rate at some point within the material measures the rate at which the distances of adjacent parcels of the material change with time in the neighborhood of that point. For this mechanism, the crackgrowth rate depends on the anodic current density via faradays laws and on the rate of repassivation at crack tips controlled by the cracktip strain rate 62, 200. Authors personal copy engineering fracture mechanics.
Quasistatic crack tip fields in ratesensitive fcc single. In conjunction with the finite element method fem or bem, it is possible to use the shape sensitivity analysis to directly evaluate the sensitivities of the total strain energy where the crack length is being treated as the shape variable. The alloy showed higher crack growth rate at 450 c due to dynamic strain ageing which causes higher stress concentration at the crack tip as compared to 600 c. Crack velocity dependent toughness in rate dependent materials. The influence of material strain rate sensitivity and void nucleation on crack tip stress and deformation fields has been evaluated for the case of a circumferentially cracked bar. With the adoption of the rate sensitive constitutive relationship, it is asymptotically investigated the propagating tip fields of plane strain.
The perfect elasticviscoplastic field at mode i quasi. Rate dependence of cracktip processes predicts twinning. Incorporating this feature produces additional strainrate sensitivity in the constitutive response. Strain rate sensitivity of alloy 718 stress corrosion cracking. Crack detection and crack propagation gages structural test labs often need to test structures to failure, stopping the applied load once a surface crack has formed in the part. Due to the local stress concentration, the tdrx is more active in the area close to the crack tip and exhibits the positive strainrate sensitivity as twinning. The materials are assumed to follow the druckerprager yield criterion and the normality. Interfacial plasticity governs strain rate sensitivity and ductility in. Mechanical characterization of eurofer97 in tension at.
Dtdhandbook fundamentals of damage tolerance fracture. Bhat a micromechanics based university of southern. With increasing crack velocity a competition exists between the strain rate hardening of the solid, which causes elevated tractions ahead of the crack tip that tend to drive crack propagation, and the rate strengthening of the fracture process zone which tends to resist fracture. Materials science and engineering a mines paristech. Betegon a a department of construction and manufacturing engineering, university of oviedo, gijon 33203, spain b department of mechanical engineering, solid mechanics, technical university of denmark, dk2800 kgs. Strain rate sensitivity describes an increase in yield strength as the testing speed increases. For cleavagelike tscc, an additional term incorporating an increment of crack growth due to mechanical fracture, e. By comparisons, when strain rate sensitivity decreases, plastic dissipation energy is reduced and the cohesive dissipation energy increases. The higher the strain rate sensitivity is, the larger amount of the external work will be transformed into plastic dissipation energy than into cohesive energy which could delay the rupturing of cohesive zone. During steadystate crack growth, elastic strains dominate asymptotically close to the crack tip if jr crack tip responds according to the pulse induced by the fast running crack. May 26, 2010 maximum cracktip temperature occurred because of crazing in a mixed mode of fracture at 1 to 1. Loading rate sensitivity of glass fiberepoxy composite at ambient and subambient temperatures.
Strain gradient plasticity modeling of hydrogen diffusion. Strain rate effects in stress corrosion cracking journal. An approximate non hardening plane strain analysis for smallscale yielding at a stationary crack tip has been given by rice 1968, as based on the slipline theory and his pathindependent line integral. Strain rate sensitivity measured at 6% strain as function of temperature for strain rates between 10. Finite element simulations are performed within a mode i, plane strain modified boundary layer framework by prescribing the two term k.
Stress corrosion crack growth rate versus crack tip strain rate for various loading. Emphasis is placed on the design of finite elements which allow accurate reproduction, m a numerical solution, of the detailed structure of the near crack tip stress and strain fields, as understood from previous analytical studies of crack tip singularities. An experimental investigation on the strain rate sensitivity of reduced activation steel eurofer97 under uniaxial tensile loads in the strain rate range from 0,001 s. Simulation of crack propagation in anisotropic structures. The kubinestrinmccormick kemc constitutive law, well suited for this kind of material response, was identified so as to model the mechanical behavior of the ferritic steel from 20 c up to 350 c. Quasistatically growing cracktip fields in elastic. The functions fx, y, t and gx, y are determined from the crack tip plasticity model employed. This work establishes criteria for material rate sensitivity and develops a new composite method for modeling constitutive response in both the rate sensitive and rate insensitive regimes for three division 5, class a materials. As a result, the total energy dissipation associated with crack extension in an elastic plastic material consists of three parts. Measurement and analysis of critical crack tip processes. This law is sensitive to both the crack tip stress.
Dynamic full field measurements of crack tip temperatures caltech. Authors personal copy engineering fracture mechanics strain. Both variable effects and measured cgr were well modeled. Strain rate dependent environment assisted cracking of.