Direct Extraction of Cohesive Fracture Properties from Digital Image Correlation: A Hybrid Inverse Technique

The accuracy of an adopted cohesive zone model (CZM) can affect the simulated fracture response significantly. The CZM has been usually obtained using global experimental response, e.g., load versus either crack opening displacement or load-line displacement. Apparently, deduction of a local material property from a global response does not provide full confidence of the adopted model. The difficulties are: (1) fundamentally, stress cannot be measured directly and the cohesive stress distribution is non-uniform; (2) accurate measurement of the full crack profile (crack opening displacement at every point) is experimentally difficult to obtain. An attractive feature of digital image correlation (DIC) is that it allows relatively accurate measurement of the whole displacement field on a flat surface. It has been utilized to measure the mode I traction-separation relation. A hybrid inverse method based on combined use of DIC and finite element method is used in this study to compute the cohesive properties of a ductile adhesive, Devcon Plastic Welder II, and a quasi-brittle plastic, G-10/FR4 Garolite. Fracture tests were conducted on single edge-notched beam specimens (SENB) under four-point bending. A full-field DIC algorithm was employed to compute the smooth and continuous displacement field, which is then used as input to a finite element model for inverse analysis through an optimization procedure. The unknown CZM is constructed using a flexible B-spline without any “a priori” assumption on the shape. The inversely computed CZMs for both materials yield consistent results. Finally, the computed CZMs are verified through fracture simulation, which shows good experimental agreement.     

Identification of Material Damage Model Parameters: an Inverse Approach Using Digital Image Processing

A reliable prediction of ductile failure in metals is still a wide-open matter of research. Several models are available in the literature, ranging from empirical criteria, porosity-based models and continuum damage mechanics (CDM). One major issue is the accurate identification of parameters which describe material behavior. For some damage models, parameter identification is more or less straightforward, being possible to perform experiments for their evaluation. For the others, direct calibration from laboratory tests is not possible, so that the approach of inverse methods is required for a proper identification. In material model calibration, the inverse approach consists in a non-linear iterative fitting of a parameter-dependent load–displacement curve (coming from a FEM simulation) on the experimental specimen response. The test is usually a tensile test on a round-notched cylindrical bar. The present paper shows a novel inverse procedure aimed to estimate the material parameters of the Gurson–Tvergaard–Needleman (GTN) porosity-based plastic damage model by means of experimental data collected using image analysis. The use of digital image processing allows to substitute the load–displacement curve with other global quantities resulting from the measuring of specimen profile during loading. The advantage of this analysis is that more data are available for calibration thus allowing a greater level of confidence and accuracy in model parameter evaluation.     

沥青混合料增量型热粘弹性本构关系研究

基于热粘弹性力学理论,就不同的温度条件下沥青混合料的应力松弛特征开展了试验研究,用广义Maxwell模型模拟沥青混合料的粘弹特性,应用热流变简单材料的时温等效原理对实验结果进行了分析和参数拟合,然后通过理论推导得到沥青混合料非定常和非均匀变温条件下增量型热粘弹性本构关系;在此基础上,给出利用此增量型应力应变本构关系进行沥青路面热粘弹性力学分析的数值实现方法,并给出一个计算实例。     

Using Semi Circular Bending Test to Evaluate Low Temperature Fracture Resistance for Asphalt Concrete

This work presents a repeatable semi circular bending (SCB) fracture test to evaluate the low temperature fracture resistance of asphalt mixture. The fracture resistance of six asphalt mixtures, which represent a combination of factors such as binder type, binder modifier, aggregate type, and air voids, and two testing conditions of loading rate and initial notch length, was evaluated by performing SCB fracture tests at three low temperatures. Fracture energy was calculated from the experimental data. Experimental results indicated strong dependence of the low temperature fracture resistance on the test temperature. Experimental plots and low coefficient of variation (COV) values from three replicates show a satisfactory repeatability from the test. The results of the analysis showed that fracture resistance of asphalt mixtures is significantly affected by type of aggregate and air void content. Experimental results also confirmed the significance of binder grade and modifier type with relation to cracking resistance of asphalt mixtures. Analysis of result also indicated that both the loading rate and initial notch length had significant effect on the fracture energy at the highest test temperature, whereas the effect was strongly diluted at the two lower temperatures. No clear trend was found with the fracture peak load from either the effect of loading rate or notch length.     

A Network Modeling Approach to Derive Unsaturated Hydraulic Properties of a Rough-Walled Fracture

The hydraulic properties of a rough-walled fracture in a limestone sample are estimated using a network model based on three-dimensional representations of the fracture apertures. Two different scenarios are considered: drainage of water out of a fracture and infiltration of water into a fracture. Besides capillary effects, the model takes into account an accessibility criterion (invasion percolation) and, in the case of infiltration, the rate dependence of the water movement. A hysteresis effect between drainage and imbibition hydraulic properties can be observed, which increases with increasing capillary number. The measured permeability is overestimated by 15% by the network model. In a sensitivity analysis the influence of the main fracture field characteristics (field size and fracture segment size in relation to correlation length) on the calculated hydraulic properties is investigated. Field size has an important influence on the inverse of the water/air entry value for imbibition, making it difficult to scale this parameter to other field sizes. A parameter analysis investigating the influence of the main fracture characteristics (mean fracture aperture, roughness, and correlation length) on the hydraulic properties shows that the mean fracture aperture is the most important fracture parameter influencing both strongly the saturated permeability K and . The effect of varying the variance and the correlation length on K and is much less than the influence of the mean fracture aperture. The effective permeability of the fracture is also calculated by the geometric mean K _g . Up to (log_e(K)) = 1, the discrepancy between K _g and K _n (network model result) is less than 15%. At larger correlation lengths (for a constant (log_e(K))), the discrepancy between K _g and K _n increases.     

Estimation of Landfill Gas Generation Rate and Gas Permeability Field of Refuse Using Inverse Modeling

Landfill methane must be captured to reduce emissions of greenhouse gases; moreover it can be used as an alternative energy source. However, despite the widespread use of landfill gas (LFG) collection systems for over three decades, little information about their capture efficiency is available, because LFG generation rates usually remain unknown. Therefore, to assess the efficiency of greenhouse gas capture and to estimate the amount of fugitive emissions, LFG generation rates should be properly determined. In addition, to improve the capture efficiency of methane while minimizing air intrusion from the atmosphere, it is important to quantify gas flow patterns within landfills. In this study, a methodology to quantify methane generation rates and to estimate the gas permeability field was examined using inverse modeling. To account for the heterogeneous, but spatially correlated structure of refuse, the pilot point method involving geostatistical techniques and optimization algorithms was used. Synthetic observation data were generated from forward simulations for a pumping test and a baro-pneumatic test, and these data were used to test the inversion procedure. The inverse model was able to reproduce the spatial permeability distribution using the transient pressure changes in response to the withdrawal of LFG during the pumping test. The LFG generation rate was also successfully estimated using the data from the baro-pneumatic test with errors less than 2%. While this methodology was developed and successfully tested using synthetic data, it will be investigated in the future using field data from the bioreactor test cells at the Yolo County Central Landfill, CA.     

Estimating the Hydraulic Conductivity of Two-Dimensional Fracture Networks Using Network Geometric Properties

Based on a modified Darcy–Brinkman–Maxwell model, a linear stability analysis of a Maxwell fluid in a horizontal porous layer heated from below by a constant flux is carried out. The non-oscillatory instability and oscillatory instability with different hydrodynamic boundaries such as rigid and free surfaces at the bottom are studied. Compared with the rigid surface cases, onset of fluid motion due to non-oscillatory instability and oscillatory instability is found to occur both more easily for the system with a free bottom surface. The critical Rayleigh number for onset of fluid motion due to non-oscillatory instability is lower with a constant flux heating bottom than with an isothermal heating bottom, but the result due to oscillatory instability is in contrast. The effects of the Darcy number, the relaxation time, and the Prandtl number on the critical Rayleigh number are also discussed.     

混凝土断裂过程区的虚拟裂纹粘聚力奇异性

混凝土断裂过程区视为具有粘聚阻力作用的虚拟裂纹，其非线性断裂和尺寸效应特性是与该虚拟裂纹粘聚力分布规律密切相关的。通过得到的粘聚应力分布函数解析结果，对该粘聚力分布特征的分析得知，在基于断裂过程区之外用线弹性场的力学模型上，该粘聚力随距离虚拟裂纹尖点的靠近，仍具有平方根奇异性。从而本文提出一个能够反映裂纹发展状态的粘聚应力奇异性强度参数，它是无粘聚力的线弹性裂纹应力强度因子和表征裂纹张开位移分布多项式参数的函数；因此，该参数可以作为混凝土非线性断裂的一个参量。文中就已有断裂试验测试结果进行了算例分析和相应的讨论。     

Estimation of Fracture Toughness of Metallic Materials Using Instrumented Indentation: Critical Indentation Stress and Strain Model

We propose a generalized approach based on fracture mechanics and contact mechanics to estimate the fracture toughness in metallic materials from instrumented indentation testing. Models were developed for brittle and ductile fracture. Different criteria were applied to each model to determine the critical fracture point during indentation. For brittle fracture, the critical fracture point was defined in terms of the critical mean pressure; for ductile fracture, the critical fracture point was derived from fracture strain and critical plastic zone size. Each fracture criterion was used to determine the indentation fracture energy corresponding to the fracture energy required for crack extension. The fracture toughness was estimated for various metallic materials using each model and compared with standard fracture toughness tests.     

Analytic Calculation of Capillary Bridge Properties Deduced as an Inverse Problem from Experimental Data

In this work, we propose an original resolution of Young–Laplace equation for capillary doublets from an inverse problem. We establish a simple explicit criterion based on the observation of the contact point, the wetting angle and the gorge radius, to classify in an exhaustive way the nature of the surface of revolution. The true shape of the admissible static bridges surface is described by parametric equations; this way of expressing the profile is practical and well efficient for calculating the binding forces, areas and volumes. Moreover, we prove that the inter-particle force may be evaluated on any section of the capillary bridge and constitutes a specific invariant.     

Mode I Fracture Characterization of Bituminous Paving Mixtures at Intermediate Service Temperatures

This study presents an integrated approach combining experimental tests and numerical modeling to characterize mode I fracture behavior of bituminous paving mixtures subjected to a wide range of loading rates at intermediate temperature conditions. A simple experimental protocol is developed using the semi-circular bending (SCB) test geometry. The local fracture behavior at the initial notch tip of the SCB specimens is monitored using high-speed cameras with a digital image correlation (DIC) system. The DIC results of the SCB fracture tests are then simulated using a finite element method that is incorporated with material viscoelasticity and cohesive zone fracture. Fracture properties are obtained locally at the notch tip by identifying two cohesive zone fracture parameters (cohesive strength and fracture energy) that result in a good agreement between test results and numerical simulations. The results clearly present significant rate-dependent fracture characteristics of bituminous paving mixtures at intermediate service temperatures. This study further demonstrates that fracture properties of viscoelastic materials need to be characterized at the local fracture process zone when they present ductile fracture behavior.     

Justification of Paris-type Fatigue Laws from Cohesive Forces Model via a Variational Approach

By using a principle of least energy and a surface energy of the Dugdale-Barenblatt type which is supplemented by an irreversibility condition, we build a debonding model of thin films valid for a monotone loadings as well as for cyclic loadings. When the internal length of the Dugdale model is small in comparison to the characteristic length of the film, we show that the growth of the debonding follows Griffith’s law under a monotone loading and a Paris-type law under a cyclic loading.     

Dynamic Fracture Properties of Titanium Alloys

Fatigue precracked specimens of three titanium alloys (6Al-4V, ELI, and Timetal 5111) were dynamically loaded in a drop weight tower system while the dynamic fracture toughness was inferred using Coherent Gradient Sensing, crack opening displacement, or strain gage methods. A comparison of the initiation toughness of the three materials as a function of loading rate and specimen thickness is made.     

Some Inverse Problems of Deformation and Fracture of Physically Nonlinear Inhomogeneous Media

The following two types of physically nonlinear inhomogeneous media are considered: linear-elastic plane with nonlinear-elastic elliptic inclusions and linear-viscous plane with elliptic inclusions from a material that possesses nonlinear-creep properties. The problem is to determine infinitely distant loads that produce a required value of the principal shear stress (in the first case) or principal shear-strain rate (in the second case) for two arbitrary inclusions. Conditions for the existence of solutions of these problems for incompressible media under plane strains are obtained.     

Characterizing Torsional Properties of Microwires Using an Automated Torsion Balance

In order to characterize the torsional behavior of microwires, an automated torsion tester is established based on the principle of torsion balance. The main challenges in developing a torsion tester at small scales are addressed. An in-situ torsional vibration method for precisely calibrating the torque meter is developed. The torsion tester permits the measurement of torque to nN m, as a function of surface shear strain to a sensitivity of sub-microstrain. Using this technique, we performed (monotonic and/or cyclic) torsion tests on polycrystalline copper and gold wires. It is found that (i) a size effect appears in both the initial yielding and the plastic flow of torsional response; (ii) a reverse plasticity occurs upon unloading in cyclic torsion response; and (iii) the Hall-Petch effect and the strain gradient effect are synergistic. We also performed cyclic torsion tests on human hairs and spider silk which are natural protein fibers with a different morphological structure to metallic wires. It is shown that the single hair exhibits torsional recovery, and that the spider silk displays torsionally superelastic behavior whereby it is able to withstand great shear strain.     

Non-Parallel Acoustic Receptivity of a Blasius Boundary Layer Using an Adjoint Approach

Localized and non-localized acoustic receptivity for a Blasius boundary layer is investigated using the adjoint Parabolized Stability Equations. The scattering of an acoustic wave onto a hump, a rectangular roughness or a wall steady blowing and suction is described. Comparisons with local approaches, triple deck theory, direct numerical simulations and experiments are successfully shown. Non-parallel effects are discussed. For comparable parameters, the non-localized receptivity problem produces amplitudes one order of magnitude larger than for the case of localized receptivity. This revised version was published online in July 2006 with corrections to the Cover Date.     

Estimation of the Geometric Parameters of a Reservoir Hydraulic Fracture

The exact solution of self-excited vibrations of a reservoir hydraulic fracture after stopping the hydraulic fracture fluid injection is obtained on the basis of the generalized hyperbolictype Perkins-Kern-Nordgren model of the development of vertical reservoir hydraulic fracture. The vibrations are excited by the rarefaction wave developed after stopping the injection. The solution obtained is used to estimate the height, the width, and the half-length of the reservoir hydraulic fracture on the basis of the field data of bottomhole pressure gauges by the time of stopping the hydraulic fracture fluid injection.     

Identification of Interaction Pressure Between Structure and Explosive with Inverse Approach

An inverse approach for the identification of the time-dependent localized interaction pressure between a structure and an explosive has been proposed and developed. In this approach, surface measurements of structural response (displacement and velocity) are integrated with numerical simulations to identify the spatial and time-dependent interaction pressure (i.e. the normal traction) on a structure surface. For verification and validation purposes, numerical simulations are used to (a) generate the time-dependent displacement and velocity fields on the free surface of the specimen at specified time intervals, (b) form a blast wave and compute the resulting interaction traction field between the structure and blast wave on the interaction interface for comparison to inverse predictions. In particular, validation of the proposed approach was performed using numerical simulation results for an underwater explosion, with excellent agreement between the identified interaction traction and the simulation generated interaction traction up to and including the maximum traction condition. To demonstrate the potential of the method, the proposed inverse procedure was employed to estimate the interaction traction field on a thin aluminum specimen subjected to transient pressure loading through detonation of explosive buried in sand.     

Optimization of Axisymmetric Membrane Shells Against Brittle Fracture

The questions investigated in this paper are related to an important class of problems of optimal design of structures against brittle fracture. The primary problem of axisymmetric shell optimization under fracture mechanics constraint is formulated as the weight (volume of the shell material) minimization under stress intensity constraints. Considered problems are characterized by incomplete information concerning crack size, crack location and its orientation. Taking into account the factor of incomplete information the paper presents the formulation of optimal shell design problem based on minimax (guaranteed) approach and provides some results of analytical investigation for thin-walled shells with through cracks.