On governing equations for crack layer propagation

Results of analysis on damage distribution of a crack layer, in a model material, supported the self-similarity hypothesis of damage evolution which has been adopted by the crack layer theory. On the basis of measurements of discontinuity density and the double layer potential technique, a solution to the crack damage interaction problem has been developed. Evaluation of the stress intensity factor illustrated the methodology. Analysis of experimental results showed that Arrhenius type constitutive relationship described very well the expansion of the active zone of a crack layer

Micromechanical study on the origin of fiber bridging under interlaminar and intralaminar mode I failure

Fiber reinforced polymers (FRPs) subjected to mode I fracture show important toughening due to the development of large scale bridging (LSB). Experimental studies of this phenomenon in unidirectional carbon/epoxy laminates using double cantilever beam specimens, demonstrate important differences in R-curve response for inter- and intralaminar fracture. Post fracture observation of composite’s cross-section pointed out dissimilar fiber bundle size and shape, as the main origin of their differences. In the present paper, representative volume elements with the composite’s constituents, based on the actual material microstructure, and homogenized 2D finite element models were developed to study the effects of microstructure on the first stage of damage leading to LSB development in carbon/epoxy composites under mode I fracture. The differences between inter- and intralaminar fracture were investigated along with the influence of fiber dispersion and the presence of interply and intraply resin-rich zones. The numerical simulations captured different microcrack morphologies for inter- and intralaminar fracture, supporting the experimental observations, while parametric studies showed the influence of the microstructure in the formation of LSB. In particular, fiber dispersion within a ply and resin rich zone between plies play significant roles in mode I fracture and can be used to control toughening mechanisms in FRPs

A Study of the Shear Response of a Lead-Free Composite Solder by Experimental and Homogenization Techniques

The current study proposes a combined experimental and modeling approach to characterize the mechanical response of composite lead-free solders. The influence of the reinforcement volume fraction on the shear response of the solder material in the joint is assessed. A novel optimized geometry for single lap shear specimens is proposed. This design minimizes the effect of plastic strain localization, leading to a significant improvement of the quality of experimental data. The constitutive model of the solder material is numerically identified from the load-displacement response of the joint by using inverse finite element identification. Experimental results for a composite solder with 0.13 reinforcement volume fraction indicate that the presence of the reinforcement leads to a 23% increase of the ultimate stress and a 50% decrease of the ultimate strain. To interpret experimental data and predict the elastoplastic response of the composite solder for varying particle volume fraction, a three-dimensional (3D) homogenization model is employed. The agreement between experiments and homogenization results leads to the conclusion that the increase in the ultimate strength and the decrease in ductility are to be attributed to load sharing between matrix material and particles with the development of a significant triaxial stress state which restricts plastic flow in the matri

Interfacial Intermetallic Growth and Strength of Composite Lead-Free Solder Alloy Through Isothermal Aging

The effects of particle reinforcement of Sn-4.0wt.%Ag-0.5wt.%Cu (SAC405) lead-free solder on interfacial intermetallic layer growth and strength of the ensuing joints through short-term isothermal aging (150°C) were studied. Composite solders were prepared by either incorporating 2wt.% Cu (3μm to 20μm) or Cu2O (∼150nm) particles into SAC405 paste. Aggressive flux had the effect of reducing the Cu2O nanoparticles into metallic Cu which subsequently reacted with the solder alloy to form the Cu6Sn5 intermetallic. While all solders had similar interfacial intermetallic growth upon reflow, both of the composite solders' growth rates slowed through aging to reach a common growth rate exponent of approximately 0.38, considerably lower than that of the nonreinforced solder (n=0.58). The nanoscale reinforced solder additionally exhibited the highest tensile strength in both the initial and aged conditions, behavior also attributed to its quick conversion to a stable microstructur

Studies on bridging tractions - simultaneous bridging tractions and COD measurements

The main objective of this work is to investigate the bridging tractions in a model composite using optical fiber Bragg grating (FBG) sensors written into selected reinforcing fibers. Simultaneously, the crack opening displacement (COD) is measured using a speckle interferometry technique. The measurements are useful in the verification of the relation between the COD and bridging tractions established with the use of the weight function method. Center crack specimens made of epoxy and reinforced with one layer of optical fibers are prepared and tested under remote tension parallel to the fibers. Bragg gratings of 0.17 to 0.38mm in length are introduced in selected fibers for direct, non invasive, local measurements of axial strains in these fibers. A controlled central crack, bridged by intact fibers, is introduced by a laser technique such that the FBGs are located between the crack faces. The results on the forces obtained from the FBGs and the COD-weight function method show good agreement. The experimental results also compare very well with 3-dimensional numerical simulations of the actual specimen geometry and loading configuratio

An elastoplastic three-dimensional homogenization model for particle reinforced composites

A model for the homogenization of the elastoplastic properties of particle reinforced composites is proposed. The microstructure is described by means of a novel technique, consisting of generating particles in a pre-existent constrained Delaunay tetrahedralization of a cubic volume by means of a modified random adsorption algorithm. This technique allows generating models with different amounts of reinforcement by using the same finite element mesh. The obtained particle morphology is similar to that of many ceramic powders often used as reinforcement. Homogenization is carried out for a typical particle reinforced metal matrix composite with reinforcement volume fractions up to 0.25 and the representative volume element size is assessed for both elastic and elastoplastic behaviours. In this latter case the representative volume element size depends on the amount of plastic strain which develops in the matrix material and a criterion to assess the model representativeness is proposed based on the amount of elastic energy stored in the composite. The predictions of the model compare well with pertinent experimental data reported in the literature. (c) 2007 Elsevier B.V. All rights reserved

Transverse cracking in the bulk and at the free edge of thin-ply composites: experiments and multiscale modelling

Thin-ply composites were shown to exhibit significantly delayed transverse cracking, but the linear onset of damage scaling with ply thickness reported by Amacher et al. (2014) did not correspond to the established LEFM based in situ strength model. This study further investigates this experimental behaviour by simultaneously comparing in situ free edge crack observation with acoustic emission measurements as well as performing ex-situ X-ray tomography observations of crack propagation. A multi-scale FE model was used to better understand the damage mechanisms at play, and showed a decreasing trend of the apparent toughness with decreasing ply thickness, which explains the deviation from the existing model. Transverse cracking at the free edges was observed to propagate quickly towards the center of the specimens for the thickest plies, while in the thinnest plies it is significantly delayed, up to a point where no cracks can reach the center of the sample before final failure

A Study of the Shear Response of a Lead-Free Composite Solder by Experimental and Homogenization Techniques

The current study proposes a combined experimental and modeling approach to characterize the mechanical response of composite lead-free solders. The influence of the reinforcement volume fraction on the shear response of the solder material in the joint is assessed. A novel optimized geometry for single lap shear specimens is proposed. This design minimizes the effect of plastic strain localization, leading to a significant improvement of the quality of experimental data. The constitutive model of the solder material is numerically identified from the load-displacement response of the joint by using inverse finite element identification. Experimental results for a composite solder with 0.13 reinforcement volume fraction indicate that the presence of the reinforcement leads to a 23% increase of the ultimate stress and a 50% decrease of the ultimate strain. To interpret experimental data and predict the elastoplastic response of the composite solder for varying particle volume fraction, a three-dimensional (3D) homogenization model is employed. The agreement between experiments and homogenization results leads to the conclusion that the increase in the ultimate strength and the decrease in ductility are to be attributed to load sharing between matrix material and particles with the development of a significant triaxial stress state which restricts plastic flow in the matrix

Interfacial intermetallic growth and strength of composite lead-free solder alloy through isothermal aging

The effects of particle reinforcement of Sn-4.0wt.%Ag-0.5wt.%Cu (SAC405) lead-free solder on interfacial intermetallic layer growth and strength of the ensuing joints through short-term isothermal aging (150 degrees C) were studied. Composite solders were prepared by either incorporating 2 wt.% Cu (3 mu m to 20 mu m) or Cu2O (similar to 150 nm) particles into SAC405 paste. Aggressive flux had the effect of reducing the Cu2O nanoparticles into metallic Cu which subsequently reacted with the solder alloy to form the Cu6Sn5 intermetallic. While all solders had similar interfacial intermetallic growth upon reflow, both of the composite solders' growth rates slowed through aging to reach a common growth rate exponent of approximately 0.38, considerably lower than that of the nonreinforced solder (n = 0.58). The nanoscale reinforced solder additionally exhibited the highest tensile strength in both the initial and aged conditions, behavior also attributed to its quick conversion to a stable microstructure