Gouging and Fracture of Engine Containment Structure under Fragment Impact

This paper presents a numerical study of the failure response of an aircraft engine containment panel obliquely impacted by a titanium turbine fragment. A three-branch Bao-Wierzbicki fracture criterion is first calibrated for the target material (2219-T851 aluminum alloy) by performing tensile tests on round bars and upsetting tests on short cylinders. With this fracture model, the finite-element simulation of the impact test successfully captures the formation of an indentation/gouging channel on the proximal surface of the panel and the growth of a crack on the distal surface. An extensive parametric study is conducted on the effect of fracture criteria, mesh size, projectile pitch angles, and finite-element codes. Deficiencies of the Johnson-Cook and the constant critical strain fracture model are identified. It is found that the numerically predicted residual thickness and mass loss of the panel are sensitive to the magnitude of the pitch angle of the projectile. A large difference in calculated energy dissipation between ABAQUS and LS-DYNA is observed.     

Experiments and Cohesive Zone Model Parameters for T650/AFR-PE-4/FM680-1 at High Temperatures

This paper reports an experimental program to establish a cohesive zone model for the T650/AFR-PE-4 (laminate) and FM680-1 (adhesive) system. The cohesive zone model is based on a four parameter characterization: in each mode, a range of values for the critical energy release rate and cohesive strength are computed from a set of experimental results. Values of each parameter are determined over the temperature range of 20–350°C. Owing to experimental limitations, two methods for determining the Mode I critical energy release rate are reported from the double cantilever beam test: the area method and the inverse method. The Mode I strength is determined from a button peel stress test. The values of the Mode II parameters are determined by using a mapping procedure that accounts for multiparameter dependence in models of the end notch flexure and single lap joint tests.     

Calibration of the SMCS Criterion for Ductile Fracture in Steels: Specimen Size Dependence and Parameter Assessment

The stress modified critical strain (SMCS) criterion provides a local index for the initiation of ductile fracture in metals as a function of plastic strain and stress triaxiality. Previous research has confirmed the SMCS criterion to be an accurate index for fracture initiation in mild steels and demonstrated its application to civil/structural engineering. To facilitate practical implementation of the SMCS criterion, two key aspects of its calibration for steel materials are examined. The first pertains to the sensitivity of the measured SMCS material toughness parameter to the size of the test coupon. New results from 23 tests of cylindrically notched tension (CNT) specimens of various sizes and notch geometries indicate that the toughness parameter is relatively insensitive to calibration specimen size. This finding validates the use of miniature bar specimens to calibrate the SMCS model for thin plate steels and in-service structures, where extraction of larger coupons is impossible. The second aspect involves the development of closed-form expressions to determine directly the SMCS toughness parameter from CNT tests, thus avoiding the need for interpretation of the test data through finite-element simulations. Based on the results of 54 numerical simulations, encompassing a range of material constitutive properties, specimen geometries, and applied deformations, a semiempirical relationship (based in part on Bridgman’s solution for necked tension rods) is proposed to determine the toughness parameter directly from the CNT bar tests.     

Mechanism behind the Size Effect Phenomenon

Size effect (SE) on quasi-brittle fracture of concrete and concretelike heterogeneous materials has been commonly demonstrated by the influence of specimen size D on the transition from strength-dominant fracture to toughness-dominant fracture for geometrically similar specimens with a common initial-crack/specimen-size ratio, i.e., a0/D = constant. Under such a condition, size D appears to be the single controlling parameter for SE. In this study, we clarify that the primary source of quasi-brittle fracture, the presence of a large fracture process zone (FPZ) in front of a crack-tip, does not follow the condition of geometry similarity even for geometrically similar specimens. This suggests that the role of FPZ is not clearly explained for SE. Therefore, this study emphasizes the interaction between FPZ and the nearest specimen/structure boundary, and the consequent SE phenomenon. The deficiencies associated with the common SE models developed by Bazant and his coworkers are discussed through comparisons with the analysis on the boundary and FPZ interaction, or the boundary effect. It is shown that quasi-brittle fracture and the transition from strength-dominant fracture to toughness-dominant fracture can occur even if specimen/structure size D is constant, i.e., size D is not the dominant factor for SE.     

Fracture Mechanics Model for Analysis of Plain and Reinforced High-Performance Concrete Beams

In developing a one-dimensional analysis and design procedure for reinforced concrete structures, research is generally based on yield phenomena and the plastic flow of steel in tension and concrete in compression. The ability of concrete to resist tension is considered in the form of tension stiffening or is completely disregarded. This procedure does not account for the influence of structural size in changing the failure mode and the stress distribution across the uncracked or cracked ligament. The key factor affecting this stress distribution is found to be the strain-softening modulus. This paper presents an improved model that is based on the fundamental equilibrium equation for the progressive failure of plain concrete beams. The concrete stress-strain relationship in tension is derived by calculating the peak tensile stress and softening modulus for different depths of beams on the basis of the fracture parameters obtained with the size effect law. Thus, the proposed model uses the peak tensile stress and the softening modulus, which vary depending on the size of the beam. To study the effect of the strength of high-performance concrete (HPC) on the concrete tensile stress-strain relationship, the experimental load-deflection plots of different-sized beams are compared with those obtained by using the proposed analytical model for eight different mixes made with locally available fly ash and slag. The model is also extended for lightly reinforced concrete beams, and the results are compared with those in the literature and are found to be in good agreement.     

Cohesive Fracturing and Stresses Caused by Hydration Heat in Massive Concrete Wall

Avoidance of cracking damage due to hydration is an important objective in the design of nuclear reactor containments. Assessment of the safety against cracking requires a realistic material model and its effective numerical implementation. Toward this goal, the paper develops a comprehensive material model which includes approximate simulation of cracking based on the principles of cohesive fracture mechanics, as well as an up-to-date creep formulation with aging and temperature effects. A standard heat conduction model is incorporated in the analysis as well. Since the crack width is the most important characteristic of cracking damage, particular attention is paid to crack spacing which governs crack width. The results of stability analysis of parallel crack systems based on fracture mechanics are used to estimate the spacing of open cracks as a function of their depth. Numerical simulations clarifying various aspects of hydration heat effects are presented.     

Proposed Method for Determining the Interval for Hands-on Inspection of Steel Bridges with Fracture Critical Members

The proposed assessment procedure presented in this paper may be used to establish inspection intervals for steel bridges with fracture critical members (FCMs) (if adopted by the Federal Highway Administration). The procedure proposed herein only applies to FCM inspections which are defined as follows: a hands-on inspection of a FCM or member components that may include visual and other nondestructive evaluations. The method is rather simple and provides an alternative procedure to the pure calendar based inspection methodology currently specified in the Code of Federal Regulations for all FCMs. There are only two requirements which must first be satisfied in order to use the assessment. The first is that the routine 24-month inspection must continue to be performed on the bridge under evaluation. The second is that a FCM inspection must be performed on the bridge or the FCM under evaluation prior to the implementation of the resulting inspection intervals given from this assessment. The “initial inspection” should be performed as a typical FCM inspection. The assessment procedure is intended to be applied to individual FCMs and not the entire bridge itself. However, on bridges with multiple FCMs, the “worst case” FCM may be evaluated using the assessment and the resulting inspection interval may be applied to all FCMs on the bridge (for simplicity and bookkeeping purposes). The decision of whether to apply the assessment to all FCMs or the bridge’s worst case FCM is left up to the owner or engineer. The approach is not based on more rigorous damage tolerant design concepts or other fracture mechanics based methods. Nevertheless, the method is a first step in providing a more rational alternative to calendar based inspection and allows owners to prioritize structures and resource allocation. Using engineering experience and judgment, the interval for the hands-on inspection of steel bridges with FCMs can then be selected based on upper limits established through a consensus. Although the focus is on fracture critical bridges and members, the writers believe that the concept could be extended to a variety of structure types and configurations.     

Random Lattice-Particle Simulation of Statistical Size Effect in Quasi-Brittle Structures Failing at Crack Initiation

The modeling of statistical size effect of concrete structures that fail at crack initiation is studied, with special attention to the interaction between the autocorrelation length and the size of the failure zone. The mechanical failure of concrete is modeled by a network of axial springs with degrading stiffness. The heterogeneity of concrete is idealized by spatial variation of the tensile strength and fracture energy. As an example, the direct tensile test in plane stress, with the size range of 1:20, is simulated. Furthermore, simulations of a four-point bending test with varying bending span are compared to the experimental results reported in the literature. The interaction of the autocorrelation length and the size of the failure zone is identified as a key parameter for the modeling of statistical size effect.     

Simple Method for Quick Estimation of Leaky-Aquifer Parameters

Simple method and explicit equations are proposed for estimating the parameters of leaky aquifers from drawdown at an observation well, which avoid the curve matching or initial estimate of the parameter. The proposed method is computationally simple and the calculations can be performed even on a handheld calculator. The application of the methods is illustrated, using published data sets. The new method yields quick and accurate estimates of the leaky-aquifer parameters, if observed drawdowns do not contain large errors. The proposed method can also analyze the early drawdowns for accurate characteristics/parameters of a confined aquifer, if the conductance of the aquitard is assigned a zero value. It is hoped that the proposed method would be of help to field engineers and practitioners.     

Dynamic Response of Closed-Loop System with Uncertain Parameters Using Interval Finite-Element Method

Using the interval finite-element method, the vibration control problem of structures with interval parameters is discussed, which is approximated by a deterministic one. Based on the first-order Taylor expansion, a method to solve the interval dynamic response of the closed-loop system is presented. The expressions of the interval stiffness and interval mass matrix are developed directly with the interval parameters. With matrix perturbation and interval extension theory, the algorithm for estimating the upper and lower bounds of dynamic responses is developed. The results are derived in terms of eigenvalues and left and right eigenvectors of the second-order systems. The present method is applied to a vibration system to illustrate the application. The effect of the different levels of uncertainties of interval parameters on responses is discussed. The comparison of the present method with the classical random perturbation is given, and the numerical results show that the present method is valid when the parameter uncertainties are small compared with the corresponding mean values.     

Retracted: Fractal Dimensions of Fracture Surfaces

Compressive strength of porous materials, especially of cement gels, has been estimated by means of fractal dimension of fracture surfaces. The relationship between mechanical strength and fractal characteristics of porous gels has been derived and tested experimentally using samples of cement gels. The dimensions of fracture surfaces have been found to be general parameters independent on the fractal dimensions of inner material components.     

Fracture Toughness of Wood Fiber Gypsum Panels from Size Effect Law

This paper addresses the size effect of inplane bending strength as well as Mode I fracture toughness and process zone length of wood fiber-reinforced gypsum panels. Wood fiber gypsum panels represent an incombustible short fiber composite material composed of recycled paper fibers embedded in a gypsum matrix. The material, which is used for sheathing and bracing of timber frame constructions, exhibits marked fracture softening supposedly resulting in a considerable size effect. In the paper presented, in a first step Ba?ant’s size effect law for quasi-brittle materials is derived. The parameters of this size effect law are then determined by means of nonlinear regression analysis applied to a test series with scaled single edge notched beam specimens. Detailed consideration is given to the adequacy of linear confidence intervals of the model parameters in comparison to nonlinear inferential results. Finally, the probability densities of fracture toughness and fracture process zone length are determined from the distributions of the size effect parameters by means of theory of random variables.     

Simulation of Crack Propagation in Asphalt Concrete Using an Intrinsic Cohesive Zone Model

This is a practical paper which consists of investigating fracture behavior in asphalt concrete using an intrinsic cohesive zone model (CZM). The separation and traction response along the cohesive zone ahead of a crack tip is governed by an exponential cohesive law specifically tailored to describe cracking in asphalt pavement materials by means of softening associated with the cohesive law. Finite-element implementation of the CZM is accomplished by means of a user subroutine using the user element capability of the ABAQUS software, which is verified by simulation of the double cantilever beam test and by comparison to closed-form solutions. The cohesive parameters of finite material strength and cohesive fracture energy are calibrated in conjunction with the single-edge notched beam [SE(B)] test. The CZM is then extended to simulate mixed-mode crack propagation in the SE(B) test. Cohesive elements are inserted over an area to allow cracks to propagate in any direction. It is shown that the simulated crack trajectory compares favorably with that of experimental results.     

Fracture Mechanics of Plate Debonding

This paper presents a fracture mechanics model to determine the load at which FRP plates will debond from reinforced concrete beams. This will obviate the need for finite-element analyses to be used in situations where there is an infinite stress concentration and where the exact details of the interface geometry and properties are unknowable. The paper shows how fracture mechanics concepts based on energy release rates, can be used to answer the question “Will this existing interface crack extend?” Possible modes of debonding are analyzed as is the effect of the plate curtailment location on the debonding mode.     

Fracture Analysis of Shear Deformable Bi-Material Interface

Based on a novel split bi-layer shear deformable beam model capable of capturing the local deformation at the crack tip, the explicit closed-form solutions of bi-material interface fracture are presented in this paper. A recently developed novel shear deformable bi-layer beam theory is briefly reviewed, from which the deformation at the crack tip is explicitly derived. A new expression for the energy release rate is then obtained using the J integral, in which several new terms associated with the transverse shear force are present; this represents an improved solution compared to the one from the classical beam model. By exploiting the two concentrated crack tip forces, the general loadings acting at the crack tip are decomposed into two groups which produce only the mode I and mode II energy release rates, respectively; the total energy release rate is thus decomposed into the mode I and II components in a global sense. The stress intensity factor referred to as local decomposition is also obtained including the transverse shear effect. The difference between the global and local mode decompositions is clarified, and a simple relationship between them is provided. The effect of the existence of a thin layer of adhesive on the stress intensity factor is further studied by an asymptotic analysis. A simple and improved expression for the T stress, the nonsingular term of stress at the crack tip, is also given. The fracture parameters of several commonly used interface fracture specimens are summarized. The present fracture analysis including the transverse shear effect is in better agreement with finite element analyses and shows advantages and improved accuracy over the available classical solutions.     

Simultaneous Zonation and Calibration of Pipe Network Parameters

A procedure for simultaneously zoning and calibrating pipe network parameters is proposed and applied to the determination of pipe resistance coefficients. The methodology is aimed at grouping the parameters of all the pipes into a small number of zone parameters, constrained to keep the difference between the computed and the measured water heads below a given tolerance. It is shown that, in the case of nonlooped networks, the methodology leads to a linear minimization problem where the objective function is a measure of the heterogeneity of the estimated parameters. In the case of looped networks an iterative procedure, where the linear problem is coupled with a nonlinear problem having a restricted number of decision variables, is proposed and demonstrated. Application of the procedure to a hypothetical example is shown. In a lab experiment, the model of a pipe network made by two different types of links has been calibrated using two measurement points and three different measured data sets, each of which was obtained by adjusting the valves located in the network to modify the pressure field. Comparison of the measured and the estimated resistance coefficients shows good correlation.     

Dynamic Fracture and Strain Rate Behavior of Aggregates Used in Transportation

The static and dynamic uniaxial compressive strengths of coarse aggregate materials used in portland cement concrete (PCC) were determined under dry and saturated conditions for three blast furnace slags, three limestones, four dolomites, and two mafic igneous rocks. The slag aggregates exhibited the lowest compressive strength, followed by the carbonates (limestones and dolomites), and the mafic igneous rocks. Both the dry and saturated aggregates revealed a higher compressive strength under dynamic loads compared to the static loads. Based on the experimental data, a rate sensitivity parameter was defined to describe the increase in compressive strength as a function of strain rate. This parameter is deemed to have considerable relevance in evaluating the ability of a specific aggregate to resist dynamic loads such as in aggregate interlock in PCC cracks and joints, friction in asphalt, and also in the development of microfracture during rock blasting. Comparison of the compressive strength data to density and LA abrasion values revealed that the dynamic data have a better correlation to the above properties than the static data.     

Structured Application of the Two-Point Method for the Estimation of Infiltration Parameters in Surface Irrigation

The two-point method is one of the best known procedures for estimating empirical infiltration parameters from surface irrigation evaluation data and mass balance, mainly because of its limited data requirements and mathematical simplicity. However, past research have shown that the method can produce inaccurate results. This paper examines the limitations of the method, reviews alternatives for improving two-point method results based on data that are collected or can easily be collected as part of a two-point evaluation, and suggests strategies for estimation and validation of results for different levels of evaluation data. Results show the limitations of formulating the estimation problem with advance data only and the benefits of using instead an advance and a postadvance mass balance relationship in the analysis. Because different combinations of parameters can satisfy the mass balance equations, the estimated function cannot be extrapolated reliably beyond the times used in formulating those relationships. While results can be used with confidence to characterize the performance of the evaluated irrigation event, they need to be used carefully for operational analysis and design purposes.     

Separation of Scales in Fracture Mechanics: From Molecular to Continuum Theory via Γ Convergence

We propose a procedure to obtain a consistent, mesh-objective, continuous model starting from chains composed of discrete springs exhibiting strain softening. Observing the size-dependent response of tensile chains and the corresponding scaling law, recent results for the variational convergence of discrete functionals (Γ convergence) are used to pass from a molecular to a continuum theory. The limit model, where softening and fracture are interpreted by the dichotomy of bulk and surface energies, reproduces the same overall properties of the discrete system. In particular, fracture energy does not vanish in the limit and the discrete approximations of the resulting continuum model are mesh objective.