A pseudo-elastic material damage model,part I: Strain energy density criterion

A failure criterion is presented which relates the strain energy density of the material to both yielding and fracture. Cumulative material damage throughout a structural component may be monitored and the relative influence of yielding and stable crack growth assessed. The criterion is demonstrated, using finite element analysis, for center cracked panel specimens differing by material toughness values. From crack growth increment predictions using the uniaxial stress-strain behavior of the material, the criterion predicts the critical value of the strain energy density factor S_c governing crack instability.     

Analytical-experimental correlation of polyaxial states of stress in Thornel-epoxy laminates

The observed strength and stress-strain response of [O₂/±45] _s Thornel-epoxy laminates under varying biaxial-stress ratios are compared with those predicted numerically. Both flat and ring-type off-axis composite specimens are employed by which to generate experimentally the biaxial data. While the numerical predictions tend to overestimate the observed laminate strengths, the several predicted stress-strain curves agree well with each other and with experiment. The off-axis ring specimens produced significantly higher strengths than did the corresponding flat specimens.     

A study of cyclic plastic stresses at a notch root

An experimental study is presented for cyclic plastic stresses at notch roots in specimens under constant-amplitude repeated tension and reversed loading. Edge-notched,K _T=2, 2024-T3 aluminum-alloy sheet specimens were cycled until local stress conditions stabilized. Local stress histories were determined by recording local strain histories during cycling and reproducting these histories in simple, unnotched specimens. The fatigue lives for these notched specimens were estimated using stabilized local stresses and an alternating vs. mean stress diagram for unnotched specimens of the same material. These predictions compared favorably with lives from S-N data for the notch configuration tested. In addition, an expression is presented for calculating local first-cycle plastic stresses. An acceptable correlation is shown between predicted stresses and experimental data within the scope of the investigation.     

Observations on Mode I and III fracture of steel and PMMA

Considered in this work are the Mode I and III fractures of W18Cr4V steel, 60Si2Mn steel and PMMA specimens. The mixed mode critical stress intensity factor, denoted by K_1f, is shown to be greater than K_1c for Mode I. The ratio K_1f/K_1c depends on the ways in which K₁ and K₃ interact and is affected by the position of the load with reference to the crack position. Analytical and experimental results are presented and discussed in connection with the microfracture surface observed experimentally.     

Analytical and experimental evaluations of the influence of fracture surface roughness,its sliding actions and the associated plasticity on fatigue crack propagation

An investigation of fatigue crack propagation in rectangular AM60B magnesium alloy plates containing an inclined through crack is presented in this paper. The behavior of fatigue crack growth in the alloy is influenced by the fracture surface roughness. Therefore, in the present investigation, a new model is developed for estimating the magnitude of the frictional stress intensity factor, k_f, arising from the mismatch of fracture surface roughness during in-plane shear. Based on the concept of k_f, the rate of fatigue crack propagation, db/dN, is postulated to be a function of the effective stress intensity factor range, Δk_eff. Subsequently, the proposed model is applied to predict crack growth due to fatigue loads. Experiments for verifying the theoretical predictions were also conducted. The results obtained are compared with those predicted using other employed mixed mode fracture criteria and the experimental data.     

A pseudo-elastic material damage model, part II: Application to the scaling of specimen size, material behavior and loading rate

A failure criterion is presented which relates the strain energy density of the material to both yielding and fracture. Cumulative material damage throughout a structural component may be monitored and the relative influence of yielding and stable crack growth assessed. The criterion is demonstrated, using finite element analysis, for center cracked panel specimens differing by material toughness values. From crack growth increment predictions using the uniaxial stress-strain behavior of the material, the criterion predicts the critical value of the strain energy density factor S_c governing crack instability.     

Measuring Fracture Energy in a Brittle Polymeric Material

The dynamic fracture behavior of a brittle polymer, polymethyl methacrylate (PMMA), was studied using single-edge-cracked tensile specimens and the method of caustics in combination with high-speed photography. The dynamic response of the specimen and the state of local stress near the crack tip, i.e., the stress intensity factor K, were measured. To analyze the dynamic response, the external work, U_ex, applied to the specimen was partitioned into three components: the elastic energy, E_e; non-elastic energy, E_n, due to viscoelastic and plastic deformation; and fracture energy, E_f, for creating a new fracture surface, A_s. The results showed that E_e, E_n, and E_f increased with U_ex, and the ratio E_f/U_ex was about 46% over a wide range of U_ex. Energy release rates were estimated using G_t = U_ex/A_s and G_f = E_f/A_s. The mean energy release rate, G_m, during dynamic crack propagation was also determined using the value of K. A good correlation between G_f and G_m was found.     

Anomalies associated with energy release parameters for cracks in piezoelectric materials

For a central crack in a piezoelectric plate, the mode-I stress intensity factor (K_I), electric displacement intensity factor (K_D), energy release rates (G, G_M) and energy density factor (S) are obtained from the finite element results. For the impermeable crack, the numerical results of K_I and K_D are coupled; this error is contrary to the uncoupled analytical solutions. The error has little effect on the total energy release rate G and energy density factor S, but in some cases, large errors in the mechanical energy release rate G_M are observed. G is global while SED is local. Also G is negative which defies physics where energy cannot be created while crack attempts to extend as implied by G. Computations should be made for the J-integral and also show that J becomes negative. What this shows is that the global fracture energy criterion is not suitable to address the local release of energy because it includes the overall energy which are irrelevant to fracture initiation being a local behavior. In addition, the case study shows that the energy density theory is the better fracture criterion for the piezoelectric material. According to the results of S, it retards the crack growth when the external electric field and piezoelectric poling are on opposite directions. This conclusion agrees with analytical and experimental evidence in the past references.     

Discrete dislocation simulations of the development of a continuum plastic zone ahead of a stationary Mode III crack

We present results from discrete dislocation simulations showing the development of the plastic zone in front of a Mode III crack under constant load. We find that the equilibrated zone is circular, in agreement with continuum mechanics predictions of the elastic-perfectly plastic Mode III crack. The size of the equilibrated zone scales as the square of the applied load (K_III), also in agreement with the continuum results. The zone approaches saturation exponentially, with a time that scales as K_III²/σ_p³, where σ_p is the Peierls stress. These results delineate conditions under which the classical, continuum predictions of elastic-plastic fracture mechanics are applicable.     

Further studies on dynamic crack branching

The newly derived dynamic-crack-branching criterion with its modifications is verified by the dynamicphotoelastic results of dynamic crack branchings in thinpolycarbonate, single-edged crack-tension specimens. Successful crack branching was observed in four specimens and unsuccessful branching in another. Crack branching consistently occurred when the necessary conditions ofK _I =K _{I b} =3.3 MPa \(\sqrt m\) and the sufficiency condition ofr _o =r _c =0.75 mm were satisfied simultaneously. In the unsuccessful branching test, the necessary condition was not satisfied sinceK _I was always less thanK _{I b} .     

A dynamic analysis of modified compact-tension specimens using homalite-100 and polycarbonate plates

The dynamic fracture and crack-arrest responses of a modified compact-tension specimen (M-CT) machined from Homalite-100 and polycarbonate sheets were studied by dynamic photoelasticity, dynamic finite-element analysis and streaking photography. In contrast to some of the published results involving steel M-CT specimens, substantial dynamic effects were observed during rapid crack propagation in the Homalite-100 and polycarbonate M-CT specimens. The dynamic crack-arrest toughnesses.K _1a , were relatively constant and were about 80 percent and 50 percent of the corresponding fracture toughness,K _1c , of Homalite-100 and polycarbonate, respectively.     

A simple model for dislocation behavior,strain and strain rate hardening evolution in deforming aluminum alloys

In this work, modeling of the stress–strain behavior is carried out using a simple dislocation model. This model uses three variables to characterize the dislocation population: The average forest and mobile dislocation densities, ρ_f and ρ_m, and the average dislocation mean free path L. However, it is shown that within reasonable assumptions, only two of these variables are independent. The mathematical form derived from this dislocation-based model was applied to experimental stress–strain data determined at room temperature for pure aluminum, 3003-O, 2008-T4, 6022-T4, 5182-O and 5032-T4 aluminum alloy sheets. The evolution of the state variables was calculated for these materials from a single stress–strain curve. The average dislocation mean free paths at a strain of 0.5 were compared with TEM observations of dislocation cell sizes or inter-dislocation spacing for specimens deformed equal biaxially with the hydraulic bulge test. A very good agreement was obtained between predictions and experiments.     

An improved experimental method for the determination of the critical stress intensity factor KIc of brittle materials

The critical stress intensity factor K_Ic is determined by a simple and accurate method, using small test specimens and a simple procedure in this paper.Single edge V-notched tension specimens made of PMMA are subjected to a load which is slowly increased until the crack begins to move from the notch tip. During the crack propagation event shadow patterns at the tip of the crack are recorded in a video recorder. Under these loading conditions, the creating real crack propagate slowly until the crack propagation velocity take an abrupt increase and the entire fracture of the specimen takes place. The stress intensity factor which correspond to the transition from the slow to fast crack speed, is the critical stress intensity factor K_Ic and it can be the fracture toughness of the material.The results are accurate and in good agreement with those values of K_Ic which are calculated by approximate theoretical expressions.The purpose of this paper is to introduce an improved, simple and accurate experimental method for the determination of fracture toughness of brittle materials.     

A moving-load controlled-displacement fracture-toughness testing machine

In conventional fracture-toughness testing, the line of application of the loads remains fixed with respect to specimen geometry. In this testing machine, the load moves with the advancing crack front, and displacement is used as the controlled variable to propagate and arrest a crack. The energy-release rate at the onset of crack propagation and, hence, the plane-strain fracture toughnessK _Ic can be measured directly without compliance calibration or stress-intensity evaluation. The specimen is in the form of a flat plat 25 by 50 cm which is simple to machine and provides about 30 values ofK _Ic. The versatility of the machine is demonstrated by making a statistical analysis ofK _Ic for 7075-T6 Al by showing the effect of plate thickness on the fracture toughnessK _c using a tapered specimen, and by evaluatingK _c in 7075 Al as a function of aging temperature in a thermal-gradient-treated specimen.     

Polymer Induced Drag Reduction in a Turbulent Pipe Flow Subjected to a Coriolis Force

The skin friction factor f in a turbulent wall-bounded flow can be greatly reduced by using polymer solutions. In this paper we discuss experimental results on the effect of the Coriolis force on turbulent drag reduction. To study this, a horizontal smooth-walled pipe with internal diameter 25?mm is placed on a horizontal table rotating about its vertical axis. The rotation is made non-dimensional with friction velocity and pipe diameter, to form the Rotation number Ro. For a range of bulk Rotation number (Ro _b ) between 0 and 0.6 for two different Reynolds numbers (Re _b = 15 & 30 × 10³), the pressure drop is measured, from which the average friction factor f is obtained. Additionally the effect of four different polymer concentrations has been investigated. The single-phase results show that the friction factor increases monotonic but gradual with Rotation. With polymer additives a drag reduction is found that increases with concentration, but which is not affected by the rotation.     

A new criterion for mixed mode fracture initiation based on the crack tip plastic core region

In this work, we propose a new criterion for mixed mode I-II crack initiation angles based on the characteristics of the plastic core region surrounding the crack tip. The shape and size of the plastic core region are thoroughly analyzed under different loading conditions and a new formulation for the non-dimensional variable radius of the core region is presented for mixed mode (K_I−K_II) fracture. The proposed criterion states that the crack extends in the direction of the local or global minimum of the plastic core region boundary depending on the resultant stress state at the crack tip. The results show a well-defined correlation between the plastic core region characteristics and crack extension angles predicted by other criteria. The proposed criterion is formulated for various loading conditions and is compared with other available criteria against the limited available experimental data. It is shown that the proposed criterion provides a better agreement with the experimental data.     

Advective Transport in Heterogeneous Formations: The Impact of Spatial Anisotropy on the Breakthrough Curve

Water flow and solute transport take place in formations of spatially variable conductivity K. The logconductivity Y?= ln K is modeled as a random stationary space function, of normal univariate pdf (of mean In K _G and variance ${\sigma_{Y}^{2}}$ ) and of axisymmetric autocorrelation of integral scales I _h,I _v (anisotropy ratio f?=?I _v/I _h?<?1). The head gradient and the velocity are uniform in the mean, parallel to bedding, and of constant and given as J and U, respectively. Transport is ruled by advection, which typically overwhelms pore scale dispersion in the breakthrough curve (BTC) determination. In the present study we analyze the impact of anisotropy f on the BTC of a passive solute, which is related to the mass flux??? (t, x) at a control plane at x. While a considerable body of literature dealt with weakly heterogeneous formations ( ${\sigma _{Y}^{2} <1 }$ ), the present study addresses the case of ${\sigma _{Y}^{2} >1 }$ , which is of interest for many aquifers and is more difficult to solve either numerically or by approximations. We approach the three dimensional problem by modeling the structure as an ensemble of densely packed oblate spheroids of semi-major and semi-minor axis R and f R, respectively, and independent lognormal K, submerged in a matrix of uniform conductivity K _ef, the effective conductivity of the ensemble. The detailed numerical simulations of transport show that the BTC is insensitive to the value of the anisotropy ratio f, i.e.,??? (t, x) I _h/U depends only on ${\sigma _{Y}^{2}}$ (except for small differences in the tail). This important result implies that transport, as quantified by BTCs or spatial longitudinal mass distributions, can be modeled accurately by the much simpler solutions developed in the past for isotropic media, like e.g., the semi-analytical self-consistent approximation.     

Experimental determination ofK I for surface cracks in a square tube under torsion

This research used the fatigue-crack-growth-rate experimental method to obtainK _I for initial semi-elliptical 45-deg inclined, longitudinal and transverse surface cracks in a hollow square tube subjected to pure torsion. Both side and corner surface cracks were investigated. Reference crack-growth-rate data using CT and SEN specimens taken from the mild-steel tubes were used in calculations. All cracks propagated in mode I on the surface at 45 deg to the longitudinal axis in the plane of the maximum tensile stress. Mixed-mode crack growth occurred subsurface for the longitudinal and transverse cracks. The experimental results were compared with other semi-elliptical surface crackK _I solutions.     

Heat transfer and skin-friction in a turbulent boundary layer under a non-equilibrium longitudinal adverse pressure gradient

The experimental data on the effect of weak and moderate non-equilibrium adverse pressure gradients (APG) on the parameters of dynamic and thermal boundary layers are presented. The Reynolds number based on the momentum thickness at the beginning of the APG region was Re^** = 5500. The APG region was a slot channel with upper wall expansion angles from 0 to 14°. The profiles of the mean and fluctuation velocity components were measured using a single-component hot-wire anemometer. The friction coefficients were determined using two methods, namely, the indirect Clauser method and the direct method of weighting the lower wall region on a single-component strain-gage balance. The heat transfer coefficients were determined by a transient method using an IR camera. It is noticed that in the pressure gradient range realized the universal logarithmic region in the boundary layer profile is conserved. The values of the relative (divided by the parameters in zero gradient flow at the same value of Re^**) friction and heat transfer coefficients, together with the Reynolds analogy factor, are determined as functions of the longitudinal pressure gradient. The values of the relative friction coefficient reduced to c_f/c_f0 = 0.7 and those of the heat transfer to St/St₀ = 0.9. A maximum value of the Reynolds analogy factor (St/St₀)/(c_f/c_f0) = 1.16 was reached for the pressure gradient parameter β = 2.9.     

钢管混凝土纯压拱失稳临界荷载计算的等效柱法

在双重非线性有限元分析的基础上,进行了钢管混凝土纯压拱失稳临界荷载的简化计算方法——等效柱法的研究,提出了等效柱法中考虑矢跨比影响的稳定系数K₁ 以及考虑初始几何缺陷影响的折减系数K₂及其与现有规范相对应的计算公式。与有限元计算结果的对比表明,采用考虑矢跨比因素的稳定系数的等效柱法能较精确地估算钢管混凝土纯压拱的非线性失稳临界荷载,且计算精度受含钢率和钢材种类变化的影响较小。