Application of the T-integral and S criteria in finite element analysis of impact damage at fastener holes in graphite/epoxy laminates under compression

This paper illustrates the application of two fracture criteria, Atluri's T^*-integral and Sih's strain energy density factor S for estimating the residual strength of an impact damaged fastener hole in a composite laminate. Finite element analyses are performed, and the magnitude and distribution of T^* and S are determined around the delamination. It is found that the profiles of these distributions are extremely complex and sensitive to the modelling of the stress fields close to the delamination. The effects of local closure, shear moduli and cracktip singularity are investigated. It is also shown that the representation of the stress singularity in the finite element model has a strong effect on the distribution of T^* and S. The distribution of both T^* and S is such that three local maxima occur and are situated at the same locations around the delamination. These locations approximately coincide with the points of maximum growth as revealed by ultrasonic C-scan of the damage growth of several specimens. The T^*-integral is shown to be more sensitive to the values of interlaminar shear moduli than S. The results of the analyses suggest that both the T^*-integral and S criteria may be successfully employed in the prediction of residual strength. However, S is better at predicting the direction of damage growth provided the stress fields near the delamination can be accurately modelled.     

Representation of the displacement rate between the loading points in terms of applied stress and temperature and its relation to creep crack growth rate, C, P and Q parameters

The displacement rate between the loading points in SUS 304 stainless steel has been experimentally obtained under several applied gross stress and high temperatures, and the equation for has been obtained experimentally as a function of applied gross stress σ_g and absolute temperature T. Then, the relation of δ to creep crack growth rate da/dt was clearly shown in terms of equation. Furthermore, the relation has been clarified between the energy rate line integral C^* as affected by , and P parameter. In this way, it is clearly shown why log (da/dt) data plotted against log C^* deviates in some systematic trend with the increase of temperature and gross stress, respectively, whereas log da/dt vs the P parameter becomes exactly the same and one straight line independent of temperature and gross stress. The discussion is made on that the similar relation will hold between the evaluation by C^* and that by _gQ or by Q^*.     

The effect of multiple damage in composite structures: a theoretical investigation

This paper focuses on the problem of damage in composite structures and discusses the theoretical analysis of the effect of multiple damaged composite laminates subject to uniaxial and bi-axial loading. The interaction effect between two 27.5 mm diameter delaminations, with 9.5 mm diameter holes, was studied using a 3-D finite element analysis as a function of damage spacing. The compressive loads required for delamination growth were predicted using a Strain Energy Release Rate approach, viz. T^*-integral. The results indicated that, for the particular layup analysed, the damage interaction can be considerable as the distance between the damage is reduced. The interaction effect appears to substantially increase T^* i.e. reduce the compressive load required for delamination growth, if the row of multiple damage is perpendicular to the applied load. T^* also appears to increase, for all the cases considered, when bi-axial loading is applied.     

On constructing T2 control charts for on-line process monitoring

In this paper we study the performance of X² control limits on T² control charts during on-line process monitoring. We make recommendations on the minimum number of subgroups necessary for control charts based on estimated parameters to perform similar to control charts based on true parameters when the X² control limit is used. We discuss an exact procedure for constructing T² control charts using estimated parameters that perform similar to control charts based on true parameters regardless of the number of preliminary subgroups. Furthermore, we suggest an implementation approach for using Alt's control limit on T² control charts until the accumulation of recommended minimum number of subgroups.     

An equivalent domain integral method for computing crack-tip integral parameters in non-elastic, thermo-mechanical fracture

The crack-tip parameters, such asJ; T^*, ΔT^* etc, which quantify the severity of the stress/strain fields near the crack-tip in elastic-plastic materials subject to thermo-mechanical loading, are often expressed as integrals over a path that is infinitesimally close to the crack-tip (front). The integrand in such integrals involves the stress-working density, stress, strain and displacement fields arbitrarily close to the crack-tip. In a numerical analysis, such data near the crack-tip are not expected to be very accurate. This paper describes simple approaches and attendant computational algorithms, wherein, the “crack-tip integral” parameters may be evaluated through “equivalent domain integrals” (EDI) alone. It is also seen that the present (EDI) approaches form the generic basis for the popular “virtual crack extension” (VCE) methods. Several examples of thermo-mechanical fracture, including: (i) thermal loading of an elastic material, (ii) arbitrary loading/unloading/reloading of an elastic-plastic material, containing a single dominant crack, are presented to illustrate the present approach and its accuracy.     

Variation Charts for Multivariate Processes

Hotelling's T² is customarily used as the control chart for multivariate SPC analysis. This chart responds to changes in both the mean values and the covariance matrix of the responses. In this article, we propose the use of a chart that concentrates on changes in the covariance matrix. The use of this covariance chart in concert with the T² chart enables the user to better determine whether T² points out of control are due to changes in mean values or due to changes in the covariance matrix. Using this chart in conjunction with T² thus furnishes a suite of tools similar to the x-bar and standard deviation charts for univariate processes.     

A theoretical framework and efficiency study of multivariate statistical process control charts

A multivariate T² chart is developed based on the Generalized Likelihood Ratio Test (GLRT) without a priori information about potential mean deviations. Identification of response variables from a T² chart is challenging and has received considerable attention recently. By highlighting the intrinsic relationship between various multivariate control charts and statistical hypothesis testing, this paper presents a theoretical framework for various individual multivariate control charts including the T² chart, regression-adjusted chart and M chart. The performance of these control charts is compared under different correlation structures among variables and different mean deviations. A hybrid control chart is also proposed based on the GLRT and union-intersection test, which can serve as a complementary diagnosis tool for the T² chart.     

Analysis of the temperature dependence of the fracture stress of sharp notched bending specimens of a structural steel with respect to intermediate transitions

The flow and fracture stresses, σ_y^g and σ_f^g (δ = crack tip displacement), of sharply notched bending specimens of a structural steel U St 37-1 are measured in the temperature range from full scale to small scale yielding. The best adaption of the experimental results for σ_f^g is obtained by a curve which exhibits an intermediate transition, i.e. which follows in a temperature range between an upper, T_tM¹ and a lower, T_tl¹, transition temperature to the curve σ_y^g(T) for the flow stress with a constant δ = δ₁. This transition corresponds to that of the slip to the twin nucleated fracture. Two analyses [3,5] according to the local fracture stress, σ_f^*, concept show that the amount and the temperature dependence of σ_f^* are somewhat different for both methods, but that both exhibit an increase of σ_f^* in the transition range. It is concluded that each transition in the nucleation mode of the fracture is connected with such a transition in the fracture stress. It may, however, become indistinct or even be covered by the scatter of the experimental points.     

Review of the fracture mechanics approach to creep crack growth in structural alloys

The application of the fracture mechanics approach to time-dependent high temperature crack growth has been reviewed. Available data on several structural alloys indicate that depending on the environmental sensitivity and creep ductility of the material, creep crack growth can be characterized by either linear elastic parameter, K, non-linear elastic-plastic parameter, J^*-integral, or reference stress, σ_ref. In particular for materials that are significantly sensitive to environment, K can adequately characterize the growth rate, and for materials that are significantly creep ductile, σ_ref can be used to predict creep life of a cracked body. Finally, for materials that are relatively ductile and wherein crack growth occurs predominantly by a deformation process, J^* integral appears to be the characterizing parameter for the growth rate. Data for several materials indicate that under steady state crack growth conditions, there may be a unique growth rate-J^* relation independent of temperature and material. This would have a profound impact in terms of the utility of fracture mechanics approach to predict creep crack growth rate and needs to be examined further. Conditions under which K, J^* or σ_ref is applicable are discussed in detail.     

On the influence of residual stresses on the fracture behavior of a structural steel in the KIc temperature range

The increase with increasing temperature of K_Ic, measured with 2CT and 1'CT specimens, from about 10³N mm at 77 K to about 2.10³ N mm at about 170 K is attributed to the increasing proportion of dimple to cleavage fracture as revealed by scanning electron microscope investigation.

The specimens were prestrained to different partial scale yielding states by the same kind of loading, performed at 298 K, as in the later K_Ictests, performed at 77 K. After pretension K_Ic = K^*_Ic is increased by a maximum amount of about half of the value K⁰_Icof nonprestrained specimens, after precompression it is reduced by the same amount if this value is evaluated from the load at which a pop-in occurs. The value K_Ic = K^**_Ic for the final fracture lies between K^*_Ic and K⁰_Ic. These results are interpretated in terms of the residual stress states due to prestraining.     

A neural network for predicting the stability of RNA/DNA hybrid duplexes

A back propagation (BP) neural network (NN) method has been developed to predict the stability of RNA/DNA duplex. Calculated T_m of hybrid formation with the present parameters fits the experimental values within reasonable errors (AD=1.2887 K, SEP=1.782, R²=0.9673 for NN1; AD=2.1388 K, SEP=3.506, R²=0.8889 for NN2). And it has the advantage that the determinations of thermodynamic parameters (TP) are not needed.     

Fracture and fatigue of bonded rubber blocks under compression

Fracture and fatigue failure of bonded rubber cylinders are discussed. Under large compressive forces, two modes of fracture are possible: splitting open of the free surface and tearing at or near the bonded edges; tearing energy T for the latter case is estimated. Under cyclic compression, the probable fracture mode of rubber is by crack propagation, leading to the bulged volume breaking away. The corresponding tearing energy is calculated. To predict the fatigue life, the rate of crack growth dc/dn is assumed to be proportional to T². A life prediction equation is thus obtained, of the form: load cycle N = (K/g)⁵, where K is a constant, about 10 for a typical soft natural rubber compound, and g is the maximum shear strain set up at the edges of the bonded surfaces.     

Moving singularity creep crack growth analysis with the (ΔT)c and C integrals

The physical meaning of (ΔT)_c and its applicability to creep crack growth are reviewed. Numerical evaluation of(ΔT)_c and C^* is discussed with results being given for compact specimen and strip geometries. A moving crack-tip singularity, creep crack growth simulation procedure is described and demonstrated. The results of several crack growth simulation analyses indicate that creep crack growth in 304 stainless steel occurs under essentially steady-state conditions. Based on this result, a simple methodology for predicting creep crack growth behavior is summarized.     

Simultaneous breakaway of a dislocation from several pinning points

The amplitude-dependent internal friction (ADIF) of very pure aluminum (99.9999%) and Al dilute alloys (20–100 ppm) has been measured at temperatures between 2 and 240 K. Two universal properties have been found in the temperature dependence of the required stress amplitude for a constant decrement. At relatively low temperatures (or high stress amplitude), the decrease of the stress with increasing temperature is proportional to T^2/3 down to 65% of the stress for 0 K, and then deviates from the T^2/3 dependence. It is explained that the elementary process is due to unpinning of a dislocation from a single solute atom. The interaction potential has been determined successfully from this region (above 40% of the stress at 0 K). At relatively high temperatures (or stress less than 40% of that for 0 K), we find for the first time that the stress changes as proportional to T⁻¹ for all dilute Al alloys but for a pure Al crystal. It is explained that the elementary process is due to simultaneous unpinning of a dislocation from several solute atoms for dilute alloys.     

Micromechanical modeling of fracture initiation in 7050 aluminum

Mechanical testing and finite element calculations have been carried out to characterize the fracture initiation behavior of the high-strength aluminum alloy 7050-T7451. Results show that fracture initiation is well predicted for two specimen types of differing constraint using the stress-modified, critical plastic strain micromechanical model. The relation between stress triaxiality and critical plastic strain was found from a series of notched tensile specimens. Data from these tests are interpreted using both companion finite element modeling and common, semi-empirical relations, and these two approaches are compared. Multiple, interrupted tests of standard, highly constrained single edge notched bend specimens are used to obtain the J–R curve in 7050 for small amounts of tearing to experimentally identify initiation. Companion modeling and the stress-modified, critical plastic strain relation are used to find the length scale for fracture, l^*, needed for initiation predictions. The calibrated stress-modified, critical plastic strain relation and length scale are then used to predict fracture initiation of a low-constraint specimen. The prediction is within 5% of the experimental measurements. Finally, various aspects of the procedure followed in the present work are compared to previous efforts using similar approaches.     

Ti-content and annealing temperature dependence of transformation behavior of TiXNi(92-XCu8 shape memory alloys

Ti-content and annealing temperature dependence of the transformation behavior of Ti_XNi_(92-X)Cu_8.0 (at,%) (X = 49.0–5l.0) alloys was investigated by varying the annealing temperature from 573 to 1273 K. It was found that the peak temperature of B2–B19 transformation (O^*) increases with increasing annealing temperature from 673 to 873 K for all of the alloys. With annealing at temperatures above 873 K, the influence of annealing on O^* depends on Ti-content. In the range of 50.4–51.0 at.% Ti, O^* shows little dependence on annealing temperature. In the range of 49.3–50.2 at.% Ti, O^* firstly decreases and then keeps constant with increasing annealing temperature. For the alloy of 49.0 at.% Ti, O^* continuously decreases with increasing annealing temperature from 873 to 1273 K. On the basis of the above data, a partial phase diagram of Ti-Ni-8.0Cu (at.%) was proposed. The transformation hysteresis also showed unique Ti-content and annealing temperature dependence.     

The (cleavage) strength of pre-cracked polycrystals

The fracture mechanics stress intensity, K, measured for the cleavage strength of carbon steel by Professor Yokobori and colleagues, at Tohoku University and elsewhere, is shown to follow a Hall-Petch dependence on average grain diameter, l, in accordance with the model-based relationship K = c's^1/2[σ₀+kl^−1/2]; for which c' is a numerical factor, 5 is the effective length of the local plastic zone associated with unstable crack growth, σ₀ is a friction stress for appropriate dislocation movement within the polycrystal grains and k is a microstructural stress intensity intermediate between that for the plastic flow or fracture of crack-free material. The separated terms in the K relationship are matched with corresponding Hall-Petch friction stress and microstructural stress intensity measurements for yielding and fracture. In this way, the K relationship is proposed to provide a bridge for the goal set some time ago by Professor Yokobori of combining the microscopic and macroscopic (continuum) viewpoints for understanding the fracture strength properties of engineering materials.     

Internal friction and elastic modulus of bulk metallic glasses

The mechanical relaxation in binary, ternary, quaternary, and quitary bulk metallic glasses with widely different glass-forming ability, or the critical cooling rate, has been studied. A single-roller melt-spinning apparatus was used for preparing thin specimens. The internal friction Q⁻¹ and the oscillation frequency f of the specimens were measured using an inverted torsion pendulum with the free decay method. The measurements were performed from room temperature, through the glass transition temperature T_g, up to the crystallization temperature T_x. As the temperature is increased, the background Q⁻¹ increases, and peaks can usually be seen near T_g and T_x. The shear modulus, which is proportional to f², is changed near the Q⁻¹ peak. The experimental data are presented and overall features of the results are discussed.     

On the aluminium hard anodization and the critical value V of the barrier layer voltage

The relation between the critical value V^* of the barrier layer voltage and the mean coordination number of the oxygen in the first coordination sphere around the aluminium atom was investigated in order to illustrate the transition from conventional to hard anodization. The modification from open to closed structure is very sharp in the neighbourhood of V^*.     

Static and dynamic finite element analysis of transformation toughening in ceramic materials

Computational studies have been conducted for the phenomenon of ‘transformation toughening’ which is observed in zirconia-containing ceramics such as PSZ (partially stabilized zirconia). The new constitutive modeling for transformation plasticity in which a stress history-dependent internal state variable is employed has been applied to the finite element analysis of stationary and growing macro-cracks under static and dynamic loading. The transformation toughening effect is discussed, along with the influence on it of the size of the transformed damage zone and the various parameters in the equations to be solved, through the observation of the behavior of the general crack tip energy release parameter, the T^*-integral.