Three dimensional (3D) microstructure-based modeling of interfacial decohesion in particle reinforced metal matrix composites

Modeling and prediction of the overall elastic–plastic response and local damage mechanisms in heterogeneous materials, in particular particle reinforced composites, is a very complex problem. Microstructural complexities such as the inhomogeneous spatial distribution of particles, irregular morphology of the particles, and anisotropy in particle orientation after secondary processing, such as extrusion, significantly affect deformation behavior. We have studied the effect of particle/matrix interface debonding in SiC particle reinforced Al alloy matrix composites with (a) actual microstructure consisting of angular SiC particles and (b) idealized ellipsoidal SiC particles. Tensile deformation in SiC particle reinforced Al matrix composites was modeled using actual microstructures reconstructed from serial sectioning approach. Interfacial debonding was modeled using user-defined cohesive zone elements. Modeling with the actual microstructure (versus idealized ellipsoids) has a significant influence on: (a) localized stresses and strains in particle and matrix, and (b) far-field strain at which localized debonding takes place. The angular particles exhibited higher degree of load transfer and are more sensitive to interfacial debonding. Larger decreases in stress are observed in the angular particles, because of the flat surfaces, normal to the loading axis, which bear load. Furthermore, simplification of particle morphology may lead to erroneous results.

An Engineering Solution for using Coarse Meshes in the Simulation of Delamination with Cohesive Zone Models

This paper presents a methodology to determine the parameters used in the simulation of delamination in composite materials using decohesion finite elements. A closed-form expression is developed to define the stiffness of the cohesive layer. A novel procedure that allows the use of coarser meshes of decohesion elements in large-scale computations is proposed. The procedure ensures that the energy dissipated by the fracture process is correctly computed. It is shown that coarse-meshed models defined using the approach proposed here yield the same results as the models with finer meshes normally used in the simulation of fracture processes

An Interface Damage Model for the Simulation of Delamination Under Variable-Mode Ratio in Composite Materials

A thermodynamically consistent damage model for the simulation of progressive delamination under variable mode ratio is presented. The model is formulated in the context of the Damage Mechanics. The constitutive equation that results from the definition of the free energy as a function of a damage variable is used to model the initiation and propagation of delamination. A new delamination initiation criterion is developed to assure that the formulation can account for changes in the loading mode in a thermodynamically consistent way. The formulation proposed accounts for crack closure effets avoiding interfacial penetration of two adjacent layers aftercomplete decohesion. The model is implemented in a finite element formulation. The numerical predictions given by the model are compared with experimental results

Processing and Composition Effects on the Fracture Behavior of Spray-Formed 7XXX Series Al Alloys

The fracture properties of high-strength spray-formed Al alloys were investigated, with consideration of the effects of elemental additions such as zinc,manganese, and chromium and the influence of the addition of SiC particulate. Fracture resistance values between 13.6 and 25.6 MPa (m)1/2 were obtained for the monolithic alloys in the T6 and T7 conditions, respectively. The alloys with SiC particulate compared well and achieved fracture resistance values between 18.7 and 25.6 MPa (m)1/2. The spray-formed materials exhibited a loss in fracture resistance (KI) compared to ingot metallurgy 7075 alloys but had an improvedperformance compared to high-solute powder metallurgy alloys of similar composition. Characterization of the fracture surfaces indicated a predominantly intergranular decohesion, possibly facilitated by the presence of incoherent particles at the grain boundary regions and by the large strength differentialbetween the matrix and precipitate zone. It is believed that at the slip band-grain boundary intersection, particularly in the presence of large dispersoids and/or inclusions, microvoid nucleation would be significantly enhanced. Differences in fracture surfaces between the alloys in the T6 and T7 condition were observed and are attributed to inhomogeneous slip distribution, which results in strain localization at grain boundaries. The best overall combination of fracture resistance properties were obtained for alloys with minimum amounts of chromium and manganese additions.

Estudio de la rotura en barras de acero : aspectos experimentales y numéricos

El acero es, junto con el hormigón, el material más ampliamente empleado en la construcción de obra civil y de edificación. Además de su elevada resistencia, su carácter dúctil resulta un aspecto de particular interés desde el punto de vista de la seguridad estructural, ya que permite redistribuir esfuerzos a elementos adyacentes y, por tanto, almacenar una mayor energía antes del colapso final de la estructura. No obstante, a pesar de su extendida utilización, todavía existen aspectos relacionados con su comportamiento en rotura que necesitan una mayor clarificación y que permitirían un mejor aprovechamiento de sus propiedades. Cuando un elemento de acero es ensayado a tracción y alcanza la carga máxima, sufre la aparición de un cuello de estricción que plantea dificultades para conocer el comportamiento del material desde dicho instante hasta la rotura. La norma ISO 6892-1, que define el método a emplear en un ensayo de tracción con materiales metálicos, establece procedimientos para determinar los parámetros relacionados con este tramo último de la curva F − E. No obstante, la definición de dichos parámetros resulta controvertida, ya que éstos presentan una baja reproducibilidad y una baja repetibilidad que resultan difíciles de explicar. En esta Tesis se busca profundizar en el conocimiento del último tramo de la curva F − E de los aceros de construcción. Para ello se ha realizado una amplia campaña experimental sobre dos aceros representativos en el campo de la construcción civil: el alambrón de partida empleado en la fabricación de alambres de pretensado y un acero empleado como refuerzo en hormigón armado. Los dos materiales analizados presentan formas de rotura diferentes: mientras el primero de ellos presenta una superficie de rotura plana con una región oscura claramente apreciable en su interior, el segundo rompe según la clásica superficie en forma de copa y cono. La rotura en forma de copa y cono ha sido ampliamente estudiada en el pasado y existen modelos de rotura que han logrado reproducirla con éxito, en especial el modelo de Gurson- Tvergaard-Needleman (GTN). En cuanto a la rotura exhibida por el primer material, en principio nada impide abordar su reproducción numérica con un modelo GTN, sin embargo, las diferencias observadas entre ambos materiales en los ensayos experimentales permiten pensar en otro criterio de rotura. En la presente Tesis se realiza una amplia campaña experimental con probetas cilíndricas fabricadas con dos aceros representativos de los empleados en construcción con comportamientos en rotura diferentes. Por un lado se analiza el alambrón de partida empleado en la fabricación de alambres de pretensado, cuyo frente de rotura es plano y perpendicular a la dirección de aplicación de la carga con una región oscura en su interior. Por otro lado, se estudian barras de acero empleadas como armadura pasiva tipo B 500 SD, cuyo frente de rotura presenta la clásica superficie en forma de copa y cono. Estos trabajos experimentales han permitido distinguir dos comportamientos en rotura claramente diferenciados entre ambos materiales y, en el caso del primer material, se ha identificado un comportamiento asemejable al exhibido por materiales frágiles. En este trabajo se plantea la hipótesis de que el primer material, cuya rotura provoca un frente de rotura plano y perpendicular a la dirección de aplicación de la carga, rompe de manera cuasifrágil como consecuencia de un proceso de decohesión, de manera que la región oscura que se observa en el centro del frente de rotura se asemeja a una entalla circular perpendicular a la dirección de aplicación de la carga. Para la reproducción numérica de la rotura exhibida por el primer material, se plantea un criterio de rotura basado en un modelo cohesivo que, como aspecto novedoso, se hace depender de la triaxialidad de tensiones, parámetro determinante en el fallo de este tipo de materiales. Este tipo de modelos presenta varias ventajas respecto a los modelos GTN habitualmente empleados. Mientras los modelos GTN precisan de numerosos parámetros para su calibración, los modelos cohesivos precisan fundamentalmente de dos parámetros para definir su curva de ablandamiento: la tensión de decohesión ft y la energía de fractura GF . Además, los parámetros de los modelos GTN no son medibles de manera experimental, mientras que GF sí lo es. En cuanto a ft, aunque no existe un método para su determinación experimental, sí resulta un parámetro más fácilmente interpretable que los empleados por los modelos GTN, que utilizan valores como el porcentaje de huecos presentes en el material para iniciar el fenómeno de coalescencia o el porcentaje de poros que provoca una pérdida total de la capacidad resistente. Para implementar este criterio de rotura se ha desarrollado un elemento de intercara cohesivo dependiente de la triaxialidad de tensiones. Se han reproducido con éxito los ensayos de tracción llevados a cabo en la campaña experimental empleando dicho elemento de intercara. Además, en estos modelos la rotura se produce fenomenológicamente de la misma manera observada en los ensayos experimentales: produciéndose una decohesión circular en torno al eje de la probeta. En definitiva, los trabajos desarrollados en esta Tesis, tanto experimentales como numéricos, contribuyen a clarificar el comportamiento de los aceros de construcción en el último tramo de la curva F − E y los mecanismos desencadenantes de la rotura final del material, aspecto que puede contribuir a un mejor aprovechamiento de las propiedades de estos aceros en el futuro y a mejorar la seguridad de las estructuras construidas con ellos. Steel is, together with concrete, the most widely used material in civil engineering works. Not only its high strength, but also its ductility is of special interest from the point of view of the structural safety, since it enables stress distribution with adjacent elements and, therefore, more energy can be stored before reaching the structural failure. However, despite of being extensively used, there are still some aspects related to its fracture behaviour that need to be clarified and that will allow for a better use of its properties. When a steel item is tested under tension and reaches the maximum load point, necking process begins, which makes difficult to define the material behaviour from that moment onward. The ISO standard 6892-1, which defines the tensile testing method for metallic materials, describes the procedures to obtain some parameters related to this last section of the F − E curve. Nevertheless, these parameters have proved to be controversial, since they have low reproducibility and repeatibility rates that are difficult to explain. This Thesis tries to deepen the knowledge of the last section of the F − E curve for construction steels. An extensive experimental campaign has been carried out with two representative steels used in civil engineering works: a steel rod used for manufacturing prestressing steel wires, before the cold-drawing process is applied, and steel bars used in reinforced concrete structures. Both materials have different fracture surfaces: while the first of them shows a flat fracture surface, perpendicular to the loading direction with a dark region in the centre of it, the second one shows the classical cup-cone fracture surface. The cup-cone fracture surface has been deeply studied in the past and different numerical models have been able to reproduce it with success, with a special mention to the Gurson-Tvergaard-Needleman model (GTN). Regarding the failure surface shown by the first material, in principle it can be numerically reproduced by a GTN model, but the differences observed between both materials in the experimental campaign suggest thinking of a different failure criterium. In the present Thesis, an extensive experimental campaign has been carried out using cylindrical specimens made of two representative construction steels with different fracture behaviours. On one hand, the initial eutectoid steel rod used for manufacturing prestressing steel wires is analysed, which presents a flat fracture surface, perpendicular to the loading direction, and with a dark region in the centre of it. On the other hand, B 500 SD steel bars, typically used in reinforced concrete structures and with the typical cup-cone fracture surface, are studied. These experimental works have allowed distinguishing two clearly different fracture behaviours between both materials and, in the case of the first one, a fragile-like behaviour has been identified. For the first material, which shows a flat fracture surface perpendicular to the loading direction, the following hypothesis is proposed in this study: a quasi-brittle fracture is developed as a consequence of a decohesion process, with the dark region acting as a circular crack perpendicular to the loading direction. To reproduce numerically the fracture behaviour shown by the first material, a failure criterium based on a cohesive model is proposed in this Thesis. As an innovative contribution, this failure criterium depends on the stress triaxiality state of the material, which is a key parameter when studying fracture in this kind of materials. This type of models have some advantages when compared to the widely used GTN models. While GTN models need a high number of parameters to be defined, cohesive models need basically two parameters to define the softening curve: the decohesion stress ft and the fracture energy GF . In addition to this, GTN models parameters cannot be measured experimentally, while GF is indeed. Regarding ft, although no experimental procedure is defined for its obtention, it has an easier interpretation than the parameters used by the GTN models like, for instance, the void volume needed for the coalescence process to start or the void volume that leads to a total loss of the bearing capacity. In order to implement this failure criterium, a triaxiality-dependent cohesive interface element has been developed. The experimental results obtained in the experimental campaign have been successfully reproduced by using this interface element. Furthermore, in these models the failure mechanism is developed in the same way as observed experimentally: with a circular decohesive process taking place around the longitudinal axis of the specimen. In summary, the works developed in this Thesis, both experimental and numerical, contribute to clarify the behaviour of construction steels in the last section of the F − E curve and the mechanisms responsible for the eventual material failure, an aspect that can lead to a better use of the properties of these steels in the future and a safety improvement in the structures built with them.

Damage localization and failure locus under biaxial loading in glass-fiber nonwoven felts

The pattern of damage localization and fracture under uniaxial and biaxial tension was studied in glass–fiber nonwoven felts. The analyses were carried out within the framework of the finite-element simulation of plain and notched specimens in which the microstructure of the felt, made up of fiber bundles connected at the cross point through an organic binder, was explicitly represented. Following previous experimental observations, fracture by interbundle decohesion and energy dissipation by frictional sliding between the bundles were included in the model. It was found that the failure path in these materials was controlled by the maximum applied normal stress, regardless of the loading path, and that the failure locus under biaxial tension was well represented by the von Mises failure criteria. The notch sensitivity of the nonwoven felts was limited and the presence of a notch did not modify the failure path.

Fatigue crack growth behaviour in molten-metal processed SiC particle-reinforced aluminium alloys

Fatigue crack initiation and subsequent short crack growth behaviour of 2014-5wt%SiC aluminium alloy composites has been examined in 4-point bend loading using smooth bar specimens. The growth rates of long fatigue cracks have also been measured at different stress ratios using pre-cracked specimens. The distributions of SiC particles and of coarse constituent particles in the matrix (which arise as a result of the molten-metal processing and relatively slow cooling rate) have been investigated. Preferential crack initiation sites were found to be SiC-matrix interfaces, SiC particles associated with constituent particles and the coarse constituent particles themselves. For microstructurally short cracks the dispersed SiC particles also act as temporary crack arresters. In the long crack growth tests, higher fatigue crack growth rates were obtained than for monolithic alloys. This effect is attributed to the contribution of void formation, due to the decohesion of SiC particles, to the fatigue crack growth process in the composite. Above crack depths of about 200 μm 'short' crack growth rates were in good agreement with the long crack data, showing a Pris exponent, m = 4 in both cases. For the long crack and short crack growth tests little effect of specimen orientation and grain size was observed on fatigue crack growth rates, but, specimen orientation affected the toughness. No effect of stress ratio in the range R = 0.2-0.5 was seen for long crack data in the Paris region.

Modelling of Stress-Corrosion Cracking by Using Peridynamics

Acknowledgement The authors are grateful to Prof. Siegfried Schmauder and Prof. Erdogan Madenci for the useful discussions that occurred throughout the realization of this study and acknowledge the Defence Science and Technology Laboratory (DSTL) for the financial support. A special thanks go to the anonymous reviewers, whose time and contribution have been highly appreciated. Results were obtained using the EPSRC funded ARCHIE-WeSt High Performance Computer (www.archie-west.ac.uk). EPSRC grant no. EP/K000586/1.