by Rességuier, T.; Signor, L.; Dragon, A.; Roy, G.

Dynamic fragmentation of shock-loaded metals is an issue of considerable importance for both basic science and a variety of technological applications, such as pyrotechnics or inertial confinement fusion, the latter involving high energy laser irradiation of thin metallic shells. Whereas spall fracture in solid materials has been extensively studied for many years, little data can be found yet about the evolution of this phenomenon after partial or full melting on compression or on release. Here, we present an investigation of dynamic fragmentation in laser shock-melted tin, from the “micro-spall” process (ejection of a cloud of fine droplets) occurring upon reflection of the compressive pulse from the target free surface, to the late rupture observed in the unspalled melted layer (leading to the formation of larger spherical fragments). Experimental results consist of time-resolved velocity measurements and post-shock observations of recovered targets and fragments. They provide original information regarding the loss of tensile strength associated with melting, the cavitation mechanism likely to occur in the melted metal, the sizes of the subsequent fragments and their ejection velocities. A theoretical description based on an energetic approach adapted to the case of a liquid metal is implemented as a failure criterion in a one-dimensional hydrocode including a multi-phase equation of state for tin. The resulting predictions of the micro-spall process are compared with experimental data. In particular, the use of a new experimental technique to quantify the fragment size distributions leads to a much better agreement with theory than previously reported. Finally, a complementary approach focused on cavitation is proposed to evaluate the role of this phenomenon in the fragmentation of the melted metal.

DOI: 10.1007/s10704-009-9378-8
Online Date: 7/29/2009
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by Bless, Stephan; Chen, Tiffany

High-velocity impact onto a layered glass target produces a very extensive damage pattern exhibiting many distinct morphologies. Material around the penetration cavity is finely comminuted. Under the arrested projectile, the glass is largely intact with spoke-like fracture regions. Around the projectile cavity, needle fragments are formed; they are radial in outer layers and circumferential in inner layers. Extensive radial cracks occur in all layers, but the spacing and frequency of transverse fractures change in each layer. Damage from radial cracks also progresses from being hoop-stress-induced to flexural-induced through the depth of the target. Fan and dicing cracks occur near the periphery of the target. Mesoscale damage features include conventional mist and hackle markings indicating very fast cracks. The map of damage presented herein should be a valuable reference for attempts to model impact damage of glass.

DOI: 10.1007/s10704-009-9379-7
Online Date: 7/28/2009
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by Khoei, A. R.; Moslemi, H.; Majd Ardakany, K.; Barani, O. R.; Azadi, H.

In this paper, an adaptive finite element procedure is presented in modeling of mixed-mode cohesive crack propagation via the modified superconvergent path recovery technique. The adaptive mesh refinement is performed based on the Zienkiewicz–Zhu error estimator. The weighted-SPR recovery technique is employed to improve the accuracy of error estimation. The Espinosa–Zavattieri bilinear cohesive zone model is applied to implement the traction-separation law. It is worth mentioning that no previous information is necessary for the path of crack growth and no region of the domain is necessary to be filled by the cohesive elements. The maximum principal stress criterion is employed for predicting the direction of extension of the cohesive crack in order to implement the cohesive elements. Several numerical examples are analyzed numerically to demonstrate the capability and efficiency of proposed computational algorithm.

DOI: 10.1007/s10704-009-9380-1
Online Date: 7/23/2009
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by Donato, Gustavo H. B.; Magnabosco, Rodrigo; Ruggieri, Claudio

This work examines the effect of weld strength mismatch on fracture toughness measurements defined by J and CTOD fracture parameters using single edge notch bend (SE(B)) specimens. A central objective of the present study is to enlarge on previous developments of J and CTOD estimation procedures for welded bend specimens based upon plastic eta factors (η) and plastic rotational factors (r

_p
). Very detailed non-linear finite element analyses for plane-strain models of standard SE(B) fracture specimens with a notch located at the center of square groove welds and in the heat affected zone provide the evolution of load with increased crack mouth opening displacement required for the estimation procedure. One key result emerging from the analyses is that levels of weld strength mismatch within the range ±20% mismatch do not affect significantly J and CTOD estimation expressions applicable to homogeneous materials, particularly for deeply cracked fracture specimens with relatively large weld grooves. The present study provides additional understanding on the effect of weld strength mismatch on J and CTOD toughness measurements while, at the same time, adding a fairly extensive body of results to determine parameters J and CTOD for different materials using bend specimens with varying geometries and mismatch levels.

DOI: 10.1007/s10704-009-9377-9
Online Date: 7/14/2009
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by Jandacka, Petr; Hlavac, Libor M; Madr, Vilem; Sancer, Jindrich; Stanek, Frantisek

This article presents a method for the experimental measurement of specific fracture energy and surface tension of a brittle materials in a powder form. This work is focused on testing a method on the mineral, almandine. A hydraulic press was used in the experiment to crush powder particles, and statistical evaluation was used to analyze the change in the powder surface. The powder was subject to various conditions during crushing. The crushing was performed both in air and in water. It was done at three different compression speeds, namely 15.8 MPa/s, 3.95 MPa/s and 2.25 MPa/s. The experimental results showed measurable differences in the specific fracture energy values in the presented regimes.

DOI: 10.1007/s10704-009-9376-x
Online Date: 7/14/2009
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by Kirk, Joshua G.; Naik, Sajo; Moosbrugger, John C.; Morrison, David J.; Volkov, D.; Sokolov, Igor

DOI: 10.1007/s10704-009-9375-y
Online Date: 7/9/2009
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by Pineda, Evan J.; Waas, Anthony M.; Bednarcyk, Brett A.; Collier, Craig S.; Yarrington, Phillip W.

A novel progressive damage and failure model for fiber reinforced laminated composites is presented in this work. The model uses the thermodynamically based Schapery Theory (ST) to model progressive microdamage in the matrix phase. Matrix failure is not governed with a matrix failure criterion, but rather matrix failure occurs naturally through the evolution of microdamage. A maximum strain criterion is used to dictate tensile failure in the fiber direction, while compressive failure is automatically accounted for by allowing local fiber rotations and tracking the evolution of rotation. The results of this model are compared to a previously developed model that used ST at the lamina level to calculate matrix microdamage, but used the Generalized Method of Cells to resolve the lamina level strains into constituent level stresses and strains and determines constituent failure by evaluating failure criteria at the micro, fiber/matrix level. Results for global load versus displacement and local strain from both models are compared to experimental data for notched laminates loaded in uniaxial tension. The results show remarkable agreement qualitatively, and in many cases the quantitative agreement is good. Accurate damage contours and failure paths are predicted.

DOI: 10.1007/s10704-009-9370-3
Online Date: 7/9/2009
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by Chiang, Chun-Ron

Trial functions based on single cylindrical inclusion solution are used todetermine the upper and lower bounds on the transverse effective thermal conductivity of a fiber-reinforced composite. Uniform size of the fibers is assumed. Comparisons are made with the bounds derived from perturbation calculations. When the fiber volume fraction is less than 0.6, the present bounds are the sharpest in terms of the width of the bounds. Specifically, the present lower bound is slightly higher than the second-order (Hashin) lowerbounds; while the present upper bound is the least of all the upper bounds.

DOI: 10.1007/s10704-009-9373-0
Online Date: 7/7/2009
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by Lavet, C.; Lapusta, Y.; Toussaint, E.; Labesse-Jied, F.; Poumarat, G.

Overall mechanical properties of bones strongly depend on their microstructure. They can be determined by developing adequate micromechanics modeling or by direct experimental measurements. Both approaches are important for a better understanding of the connection between the bone’s microstructure and resulting macro-properties. In this work, a simple experimental method is proposed for the determination of the longitudinal Young’s modulus and Poisson’s coefficient of small, and especially short, bones, based on a combination of compression and grid method. The developed experimental set-up allows measuring the displacement and strain distribution on the surface of the bone sample subjected to a compressive test, as well as the longitudinal Young’s modulus and Poisson’s coefficient. Some results for the determined macroproperties of small bones are presented and compared with the results obtained using a more sophisticated method – the Digital Image Correlation (DIC) one.

DOI: 10.1007/s10704-009-9372-1
Online Date: 7/7/2009
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by Cherepanov, Genady P.

Self-sustaining fracture waves hypothesized by Galin and Cherepanov (1966) have been observed in shock-compressed glasses and in Prince Rupert’s drops, but their speed did not correspond to the predicted value. This controversy is addressed in the present note. We now assume that this speed is equal to the local velocity of sound in the particulate material just behind the wave front, and show that, then, it is in a reasonable agreement with test data. The specific heat spent on the self-sustaining fracture wave in soda lime glass is estimated to be 1 to 20 J/g for moderately high pressures.

DOI: 10.1007/s10704-009-9371-2
Online Date: 7/7/2009
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