Analysis of temperature distribution near the crack tip under constant amplitude loading

Abstract

A B S T R A C T An analytical/numerical method has been developed to find the temperature rise near the crack tip under fatigue loading. The cyclic plastic zone ahead of the crack tip is assumed to be the shape of the source of heat generation and some fraction of plastic work done in cyclic plastic zone as heat generation. Plastic work during fatigue load was found by obtaining stress and strain distribution within the plastic zone by Hutchinson, Rice and Rosengren (HRR) crack tip singularity fields applied to small scale yielding on the cyclic stress strain curve. A two-dimensional conduction heat transfer equation, in moving coordinates, was used to obtain temperature distribution around the crack tip. Temperature rise was found to be a function of frequency of loading, applied stress intensity factor and thermal properties of the material. A power-law relation was found between the rise in temperature at a fixed point near the crack tip and range of stress intensity factor.Keywords crack tip; plastic strain energy density; point source; temperature rise. N O M E N C L A T U R Ea = Crack length, m da/dN = Crack growth rate, m/cycle t = Time, s v = Velocity of the crack tip =ȧ(t), ms −1 n = Cyclic strain hardening exponent k = Cyclic strength coefficient, Pa q = Heat generation per unit growth of the crack, Jm −2 q = Rate of heat generation per unit volume, Jm −3 -s E = Modulus of elasticity, Pa I n = Non-dimensional parameter of exponent n K I = K Imax − K Imin = Range of stress intensity factor under mode I loading, MPa (m) 1/2 σ ∞ = Range of remotely applied load, (= σ max -σ min ), Pa F = A function of geometry of the specimen = Frequency of loading, cycle/s σ 0 = Cyclic yield stress ( σ 0 ∼ 2σ 0 ), Pa σ ij = Range of stress ahead of crack tip, i, j = r, θ, z in Polar co-ordinate and x, y and z in Cartesian co-ordinate, Pa. Subscript eq = equivalent ε p ij = Range of plastic strain ahead of crack tip, i, j = r, θ , z in Polar co-ordinate and x, y and z in Cartesian co-ordinate. Subscript

Electromagnetic Emissions from Quartz Subjected to Shear Stress: Spectral Signatures and Geophysical Implications

“…This has been observed by several authors on various minerals. Some Authors [32,33] observed the propagation of the fracture in quartz crystals with optical spectrometers; calculated the final temperature, which exceeded 1700 • C. As a consequence of this heating, a melting flash is generated and the density of the molten material decreases, corresponding to an increase in volume. In fact, from the SEM images (Figure 4) it is noted that the fractures form a ridge with respect to the surface: in Figure 4 particle of about 100 × 100 µm is observed, with a thickness of about 15 µm, on whose surface there are various fractures, which they tend to bifurcate several times, forming ridges between a few tens of nm in height, up to 0.7 µm at the first bifurcation.…”

Research on fatigue crack propagation behaviour of 4003 ferritic stainless steel based on infrared thermography

“…Therefore, mobile heat source should be introduced in this situation. Then temperature variation can be showed by Eq : with q the dissipated power per unit length of crack front, r the distance to the heat source, the heat diffusivity, v the crack propagation velocity, K 0 the modified Bessel function of the second kind and zero order with argument . Then, known from Eqs and , the temperature rise near the crack tip is a function of the Δ K , the frequency of loading f , the crack speed v and the thermal conductivity of the material k .…”

“…Therefore, mobile heat source should be introduced in this situation. Then temperature variation can be showed 24,27 by Eq (7):…”

“…In the authors' next paper, the thermal effect of plastic dissipation at the crack tip on the stress intensity factor has been studied, the analytical process showed that the temperature rise is proportional to the dissipated power, while this paper focused on the effects of the thermal stresses. Pandey KN et al . proposed a numerical method to study the temperature rise near the crack tip under fatigue loads, the result showed that the temperature rise near the crack tip is a function of the Δ K , the frequency of loading, the crack speed and the thermal conductivity of the material.…”

Cyclic deformation behaviour, microstructural evolution and fatigue life of duplex steel AISI 329 LN

“…However, various experimental techniques are available to determine cyclic stress-strain curves of metallic materials [1]. In recent years, it has become more and more common to supplement the acquisition of fatigue data by additional thermal [3][4][5][6][7][8] and electrical [9][10][11][12][13] measurements. The application of thermographic methods on cyclically loaded steel specimens is reported for instance in [4], the determination of the fatigue limit on the basis of energy dissipation is described in [7].…”