Mixed mode fatigue crack growth predictions

This work is aimed at developing a predictive capability for the quantitative assessment of crack growth under fatigue loadings. The crack growth rate relation, $\text{Δa}\text{ΔN}$, may involve all three stress intensity factors k₁-k₃ such that the direction of crack growth may not be known in advance and must be predicted from a preassumed criterion. In principle, both the stress amplitude and the mean stress level should be included in the original expression for $\text{Δa}\text{ΔN}$.The strain energy density factor range, ΔS, is found to be a convenient parameter for predicting fatigue crack growth and can be applied expediently to examine the combined influence of crack geometry, complex loadings and material properties. Assumed is the accumulation of energy, $\text{ΔW}\text{ΔV}$, stored in an element ahead of the crack which triggers subcritical crack growth upon reaching a number of loading cycle, say ΔN. The proposed $\text{δa}\text{ΔN}$ relationship includes both the stress amplitude and mean stress effects.     

A fracture criterion for three-dimensional crack problems

A criterion for predicting the growth of three-dimensional cracks is developed on the basis of the strain energy density concept which has been used successfully for treating two-dimensional crack problems. Fracture is assumed to initiate from the nearest neighbor element located by a set of spherical coordinates (r, θ, φ) attached to the crack border. The new fracture surface is described by a locus of these elements whose locations correspond to the strain energy function, dW/dV, being a minimum. The function dW/dV is found to be singular of the type 1/r and is of quadratic form in the three stress intensity factors k₁, k₂ and k₃ expressed through the strain energy density factor S. It is postulated that unstable crack propagation initiates from a region where S reaches a critical value S_cr = r₀(dW/dV)_cr. The locations of failure lying on the fracture surface is determined by holding (dW/dV)_cr = S_min/r₀ constant. The quantity S_min stands for the value of S minimized with respect to θ and φ and r₀ is a radial distance measured from the crack border.

An example of failure prediction for an embedded elliptical crack subjected to both normal and shear loads is presented. According to the S-criterion, fracture initiation takes place at the ends of the minor axis. An unexpected result is that for a narrow elliptical crack and Poisson's ratio of 1/3 the lowest failure load occurs when the uniaxial tensile load makes an angle of approximately 60° with the crack surface and is in the plane of the major axis. This is in contrast to the expectation that the lowest critical load occurs when the uniaxial tension is perpendicular to the crack surface. In the limit as the elliptical crack becomes increasingly narrower, the result reduces to the two dimensional line crack case of Mode I and III loading. The S-criterion is also applied to the failure prediction of three dimensional cracks under compressive loads.     

Dynamic analysis for two-dimensional multiple crack division

Based on the concept of linear-elastic fracture mechanics, two dynamic adjustments are made upon the static form of the crack-extension force ζ for the problem of evenly spaced radial cracks spreading out from a point and terminating on a circular locus. The first adjustment is concerned with the magnitude of the local dynamic stress tending to open the crack. This dynamic stress can be approximated by the circumferential stress near a circular locus of stress relief expanding at a constant speed provided that the arc length between adjacent crack ends is sufficiently small in comparison with the circle radius. The second adjustment is concerned with the influence of crack speed on the crack-opening displacement and on the rate of release of stress field energy, ζ. This can be determined by application of the crack closure method for a traveling crack. These two dynamic adjustments are found to be opposite in direction. The degree of compensation depends on the speed of crack propagation and the Poisson's ratio of the material.     

Gabriel: a design environment for DSP

Gabriel, a second-generation digital signal-processing (DSP) design environment, is described. The Gabriel experimental signal-processing software performs non-real-time algorithm simulations and code synthesis for real-time hardware based on programmable DSPs. Gabriel eases code development for architectures that are not easy targets for conventional compilers. The model of compilation used by Gabriel is discussed at length. Modification of the model to run in real time, target architectures, and scheduling are examined     

Short and long crack data for fatigue of 2024‐T3 Al sheets: binariness of scale segmentation in space and time

Pedagogically speaking, crack initiation–growth–termination (IGT) belongs to the process of fracture, the modelling of which entails multiscaling in space and time. This applies to loadings that are increased monotonically or repeated cyclically. Short and long crack data are required to describe IGT for scale ranges from nano to macro, segmented by the SI system of measurement. Unless the data at the nano scale can be connected with the macro, IGT remains disintegrated. The diversity of non‐homogeneity of the physical properties at the different scale ranges results in non‐equilibrium. These effects dubbed as non‐equilibrium and non‐homogeneous are hidden in the test specimens and must be realized. They can be locked into the reference state of measurement at the mi‐ma scale range by application of the transitional functions and transferred to the nano‐micro and macro‐large scale ranges. The aim of this work is to convert the ordinary crack length data to those referred to as short cracks that are not directly measurable. All test data are material, loading and geometry (MLG) specific. The results obtained for the 2024‐T3 aluminium sheets hold only for the MLG tested. The differences are more pronounced for the short cracks. These effects can be revealed by comparing the incremental crack driving force (CDF) for the ma‐mi range the ma‐large range and the na‐mi range The CDF is equivalent to the incremental volume energy density factor (VEDF). The incremental mi‐ma CDF is found to be 10–10⁵ kg mm^?1 for cracks 3–55 mm long travelling at an average velocity of 10^?5 mm s^?1. The crack velocity rises to 10^?3 mm s^?1 when the incremental CDF is increased to 10⁵–10⁶ kg mm^?1, while the crack lengths are 49–260 mm. The crack velocity for the na‐mi range of 0.040–0.043 mm slowed down to 10^?8 mm s^?1, and the incremental CDF reduces further to 10^?8–10^?2 kg mm^?1. Note that changed several orders of magnitude while the crack advanced from 0.040 to 0.044 mm. Such behaviour is indicative of the highly unstable nature of nanocracks. All results are based on using the transitionalized crack length (TCL). The TCL fatigue crack growth increment Δa is postulated to depend on the incremental CDF ΔS or ΔVEDF. The form invariance of , and is invoked by scale segmentation to reveal the multiscale nature of IGT that is inherent to fatigue crack growth. While the choice of directionality from micro to macro is not the same as that from macro to micro, this difference will not be addressed in this work.     

An approximate three-dimensional theory of layered plates containing through thickness cracks

The objective of this investigation is the development of an approximate three-dimensional theory of laminated plates for application to laminates containing through-the-thickness cracks. This is accomplished by assuming an approximate form for the stress field as a product of a function of the out-of-plane variables. The variational principle of minimum complementary potential energy is employed to obtain a system of partial differential equations and associated boundary conditions which govern the in-plane variation of the stress field. This approximate theory is then applied to the problem of a laminar composite plate containing a through-the-thickness crack subjected to in-plane loading normal to the crack face. The resulting mixed boundary value problem is solved by integral transform methods. The stress field in the vicinity of the crack edge is obtained in closed form demonstrating qualitative features characteristic of the exact three-dimensional asymptotic solution. The through-the-thickness variation of this stress field is chosen so as to enforce plane strain conditions within each layer of the composite plate.The results indicate the influence of the geometric parameters and material properties of the composite system on the amplitude and transverse variation of the stress field in the vicinity of the leading crack edge.     

Transient hygrothermal stresses in composites: Coupling of moisture and heat with temperature varying diffusivity

In this paper, the influence of coupled diffusion of heat and moisture on the transient stresses in a composite is investigated analytically where the moisture diffusion coefficient is taken to be temperature dependent while the thermal diffusion coefficient is kept constant. There is no a priori reason why moisture and temperature should be uncoupled such that each will obey the simple diffusion theory, particularly without reference made to the initial and boundary conditions of a particular situation. A study of the coupled diffusion equations were made by a finite-difference scheme allowing for time-dependent changes in the humidity and temperature of the environment. The appropriate transient boundary conditions are specified on the surfaces of an infinite plate. Numerical calculations were carried out for the T300/5208 graphite fiber-reinforced epoxy matrix composite in which the nonuniformity of moisture and temperature is evaluated for sudden changes in the surface moisture and/or temperature. The coupling effect between temperature and moisture is found to be most significant when the plate undergoes a sudden change in surface temperature while the surface moisture concentration is held constant. The present findings indicate that the stresses due to coupling can deviate from the uncoupled results anywhere from 20 to 80% depending on the surface temperature gradient. This suggests the need to perform additional experiments for evaluating the coupled diffusion phenomenon and its influence on the mechanical behavior of epoxy-resin-composites.     

Effect of material nonhomogeneity on crack propagation characteristics

The influence of material nonhomogeneity on the behavior of a moving crack is investigated. The model assumes a running crack in a material whose elastic properties may differ from those of the surrounding material. Theoretical calculations showed that the energy stored in elements ahead of the crack can be raised or lowered depending on the crack velocity, the crack length and the degree of material nonhomogeneity which is associated with the ratio of the shear moduli and the distance between the crack and the neighboring material with different elastic properties. Based on the strain energy density theory, predictions are made on how material nonhomogeneity can influence the initiation and/or arrest characteristics of cracks.     

The influence of the soret and dufour effects on the diffusion of heat and moisture in solids

Phenomenological arguments leading to coupled equations governing simultaneous diffusion of moisture and heat in a solid are presented. The coefficients are related to basic thermodynamic properties of the solid, including the heat of transport associated with the Dufour effect. By Onsager's reciprocal relations, the reciprocal Soret effect, or thermal diffusion, is also related to the heat of transport. The solution of the problem of diffusion into a thick slab of material due to sudden changes in temperature or moisture at the surfaces of the slab is given. Relationships between effective diffusion coefficients in diffusion experiments and the constants of the theory are also included. The initial rate of absorption of moisture in the case of constant surface temperature is about the same as given by the uncoupled theory, with very little accompanying absorption of heat. For constant surface moisture concentration, however, a diffusion of moisture accompanies the diffusion of heat, both taking place at a rate initially corresponding approximately to the coefficient of diffusion of heat.