Damage Delocalization Research Articles

How crack twisting in bouligand structures lead to damage delocalization and toughening

Fiber-reinforced composites with Bouligand structure exhibit remarkable mechanical properties due to the intricate arrangement of fibers. In this study, we propose a coarse-graining (CG) model specifically developed to capture the behavior of Bouligand structures. The model incorporates bonded interactions to represent the fibers and employs a double-well potential to describe the non-bonded interactions within the matrix. Using this model, we investigate the fracture mechanics properties of Bouligand structures, with a particular focus on the emergence of helicoidal cracks. Our primary objective is to validate the hypothesis that these twisting cracks, which align with the fiber orientation, contribute to local hardening mechanisms. By hindering the growth of individual cracks, these hardening mechanisms facilitate the nucleation and growth of multiple cracks, thereby promoting a delocalization effect within the material. Through extensive simulations and analysis, we confirm the validity of our hypothesis. The presence of twisting cracks indeed induces local hardening mechanisms, making it more challenging for individual cracks to propagate. This phenomenon effectively spreads the damage, dissipating energy across larger volumes of the material. Consequently, the toughness of these Bouligand structures is enhanced, as this delocalization effect effectively mitigates the concentration of damage. These findings provide valuable insights into the fracture behavior of Bouligand structures and shed light into the underlying mechanisms responsible for their exceptional mechanical performance. Moreover, our CG model offers a practical and efficient approach to studying and understanding the fracture mechanics properties of complex fiber-reinforced composites. The ability to simulate and analyze the behavior of helicoidal cracks within Bouligand structures opens up new avenues for designing and optimizing advanced materials with enhanced toughness and damage resistance.

Effects of a nonlocal microstructure on peeling of thin films

In this work, starting from an approach previously proposed by the Authors, we put forward an extension to the large deformation regime of the dimensionally-reduced formulation for peridynamic thin plates, including both hyperelasticity and fracture. In particular, the model, validated against numerical simulations, addresses the problem of the peeling in nonlocal thin films, which when attached to a soft substrate highlights how nonlocality of the peeled-off layer might greatly influence the whole structural response and induce some unforeseen mechanical behaviours that could be useful for engineering applications. Through a key benchmark example, we in fact demonstrate that de-localization of damage and less destructive failure modes take place, these effects suggesting the possibility of ad hoc conceiving specific networks of nonlocal interactions between material particles, corresponding to lattice-equivalent structure of the nonlocal model treated, of interest in designing new material systems and interfaces with enhanced toughness and adhesive properties.

Moving from theory to application: Evaluating the numerical implementation of void shape effects and damage delocalization in the modeling of ductile fracture in porous plastic metals

In this paper, we present a robust exploration of the Gologanu–Leblond–Devaux (GLD) model, an advanced iteration of the Gurson model, designed to predict ductile fractures in porous metals. Going beyond the limits of the original Gurson model, the GLD model accounts for cavity shape effects and non-local strain localization, marking a significant leap in fracture mechanics. We also present a comprehensive exposition of the GLD model and its non-local extension, establishing their compatibility with the concept of GSMs. Notably, we emphasize the uniqueness of solutions in the numerical implementation, underlining the imperative need for a meticulously devised mixed implicit/explicit algorithm. Furthermore, we set out to validate the GLD model through rigorous comparisons of our numerical simulations with experimental data. Employing a damage delocalization approach rooted in the natural logarithm of porosity, our study provides compelling evidence of the model’s performance. This approach mitigates issues observed with the original porosity rate, preventing excessive smoothing of porosity and maintaining the fidelity of stress–strain curves. In addition, we gave a profound theoretical elucidation of this phenomenon via Fourier’s analysis of porosity rate. Through this work, we not only enhance our understanding of ductile fracture behavior but also establish a robust numerical framework for its predictive modeling. The GLD model emerges as a powerful tool for the accurate analysis and prediction of fracture phenomena in porous materials, further advancing the field of materials science and engineering.

Effect of ion-induced nuclear reactions on structure modification and radiolysis in LiF irradiated by 410 MeV 36S ions

The objective of this research is to study the structural damage in LiF crystals irradiated with 410 MeV 36S ions. We report on the appearance of a remarkable structural damage far (hundreds of μm) beyond the penetration depth (136 μm) of sulfur ions. Selective chemical etching on samples irradiated at room temperature revealed the formation of extended defects within the ion-irradiated zone and also beyond the range of sulfur ions. Based on AFM image analysis, the defects were identified as nano-size colloids (10 nm). In the irradiated zone, nanoindentation tests indicated a significant hardening effect. Annealing experiments showed manifestations of intense radiolysis both in the ion-irradiated and beyond the range areas with a maximum of around 620 K. Comparison of experimental results with those of performed model simulation using Monte-Carlo particle transport code FLUKA support the assumption that the cause of the observed long-range damage is irradiation by secondary particles created in inelastic nuclear collisions between incident sulfur ions and lithium and fluorine nuclei of the target atoms. Neutrons, γ-rays and protons are rated as the dominating components of the secondary particle flux. The results can be helpful for assessing the risks for damage delocalization and for reasonable selection of ions in the applications of ion technologies to optical materials like LiF.

Modulation of impact energy dissipation in biomimetic helicoidal composites

Biologically composites offer inspiration for the design of next generation structural materials due to their hierarchical microstructure that allows for, low density, and combination of high stiffness and toughness, currently unmatched by engineering technologies. Here, we investigate biomimetic composite materials that feature the laminated helicoidal architecture of fibers characteristic of the arthropod cuticle, specific to the mantis shrimp, but utilize either glass or Kevlar fibers, with epoxy or urethane matrix materials, to examine their role in impact energy dissipation. Drop weight impact test revealed epoxy-matrix composites exhibited the highest peak load on impact and showed larger degrees of external damage such as delamination and fiber breakage as compared to the urethane-based composites. Moreover, the helicoidal panels, showed a significant reduction in dent depth and better residual compressive strength as compared to the quasi-isotropic design. These findings provide useful insight into the variation of reinforcement and matrix materials for the helicoidal architecture and how it affects the delocalization of damage and improves residual strength.

Enhancing Strength and Toughness of Hierarchical Composites through Optimization of Position and Orientation of Nanotubes: A Computational Study

Hierarchical composites that combine microscopic fibers and carbon nanotubes (CNTs) offer opportunities to further improve mechanical properties. Motivated by the experimental evidence that the spatial distribution of CNTs has a significant effect on the strength and toughness of these composites, we developed a novel modelling tool to help us explore mechanisms of strengthening and toughening in an efficient way. The spatial position and orientation of CNTs are chosen as design variables and their optimization is performed on the example of a unidirectional fiber-reinforced composite (FRC) subjected to transverse tensile loading. The model relies on the use of genetic algorithm and finite element method. Our modelling results show that the CNT network with an optimized morphology suppresses stress concentrations in the matrix near the fibers. The optimized morphology is shown to activate a new strengthening and toughening mechanism—diffusion of damage at micro-scale. It allows substantial increase in the consumption of the strain energy by matrix cracking, delocalization of damage, and with it, improvement of the strength and toughness. When the network morphology of 1.0 wt% of CNTs is optimized, the strength and toughness are increased by 49% and 65%, respectively, compared to the pristine FRC. The same amount of homogenously distributed CNTs in the composite leads to only 2% of the strength increase accompanied by a 13% decrease in toughness. The work emphasizes the importance of optimizing spatial position and orientation of CNTs for the strength and toughness improvements of composites.

Additive Manufacturing and Performance of Architectured Cement-Based Materials.

There is an increasing interest in hierarchical design and additive manufacturing (AM) of cement-based materials. However, the brittle behavior of these materials and the presence of interfaces from the AM process currently present a major challenge. Contrary to the commonly adopted approach in AM of cement-based materials to eliminate the interfaces in 3D-printed hardened cement paste (hcp) elements, this work focuses on harnessing the heterogeneous interfaces by employing novel architectures (based on bioinspired Bouligand structures). These architectures are found to generate unique damage mechanisms, which allow inherently brittle hcp materials to attain flaw-tolerant properties and novel performance characteristics. It is hypothesized that combining heterogeneous interfaces with carefully designed architectures promotes such damage mechanisms as, among others, interfacial microcracking and crack twisting. This, in turn, leads to damage delocalization in brittle 3D-printed architectured hcp and therefore results in quasi-brittle behavior, enhanced fracture and damage tolerance, and unique load-displacement response, all without sacrificing strength. It is further found that in addition to delocalization of the cracks, the Bouligand architectures can also enhance work of failure and inelastic deflection of the architectured hcp elements by over 50% when compared to traditionally cast elements from the same materials.

A highly stretchable double-network composite.

Inspired by the toughening mechanism of double-network (DN) hydrogels, a soft composite consisting of a fabric mesh and VHB tape layers was fabricated. The composite was as stiff as the fabric mesh, and as stretchable as the VHB tape. At certain compositions, the composite was significantly stronger and tougher than the base materials. The extensibility and toughness of the composite can be attributed to a damage delocalization mechanism similar to that of the DN gels. In the partially damaged regions, the fabric mesh fragmented into small islands, surrounded by the highly stretched VHB tapes. Accommodated by the finite sliding at the interface, the large deformation of the composite is highly non-affine. Just as the DN gels, the coexistence of the partially damaged and intact regions resulted in a stable necking in the composite when subjected to uniaxial tension. The propagation of the necking zone corresponded to a plateau on the stress-stretch curve. During cyclic loading, the composite also exhibited stress hysteresis with almost recoverable strain, similar to that in a DN gel. To rationalize these observations and to better understand the underlying physical mechanism, a simple 1D model has been developed for the damage evolution process in the composite. The predictions of the model have achieved good agreement with the measured properties of the composite of various compositions. Furthermore, the composite itself may also be regarded as a macroscopic model when studying the properties and toughening mechanism of the DN gels.

An improved nonlocal Gurson model for plastic porous solids, with an application to the simulation of ductile rupture tests

In recent work, the author and co-workers have developed a new methodology to delocalize the damage in Gurson model for porous ductile materials. The motivation was to rectify the difficulties connected to the excessive damage smoothing arising in the practical use of the original damage delocalization method. The new approach consists of delocalizing the logarithm of the damage instead of the damage itself. The relevance of the new method to avoid mesh size effects and satisfactorily reproduce typical ductile fracture experiments are explored in this work.

Damage smoothing effects in a delocalized rate sensitivity model for metals

It has been long time established that application of damage delocalization method to softening constitutive models yields numerical results that are independent of the size of the finite element. However, the prediction of real-world large and small scale problems using the delocalization method remains in its infancy. One of the drawbacks encountered is that the predicted load versus displacement curve suddenly drops, as a result of excessive smoothing of the damage. The present paper studies this unwanted effect for a delocalized plasticity/damage model for metallic materials. We use some theoretical arguments to explain the failure of the delocalized model considered, following which a simple remedy is proposed to deal with it. Future works involve the numerical implementation of the new version of the delocalized model in order to assess its ability to reproduce real-world problems.

An Impact Protective Structure with Bistable Links

This article discusses a protective structure of a special morphology with an advanced impact resistance. We use a ‘bistable’ structure that is designed to have a non-unique stress–strain relation. When the strain reaches a threshold, some parts (sacrificial elements) yield and subsequently fail and the remaining parts (waiting elements) become active; the waiting elements carry the load and preserve structural integrity. Damage in bistable structures is more stable; the cracks do not develop due to yielding of structural elements and damage delocalization. The damage spreads in a larger region than in a conventional structure, and the load is redistributed. As a result of these effects, more impact energy is absorbed. We describe the response of bistable structures in macro- and microscales, numerically investigate a problem of projectile impacting a protective net, and introduce a mesoscale damage tensor that measures the degree of damage in a small region. We compare the structural responses of the bistable and conventional structure depending on mass and speed of the projectile. Typically, the bistable structure dissipates more energy by creating a partial damage in a large area.

Transition waves in bistable structures. II. Analytical solution: wave speed and energy dissipation

We consider dynamics of chains of rigid masses connected by links described by irreversible, piecewise linear constitutive relation: the force–elongation diagram consists of two stable branches with a jump discontinuity at the transition point. The transition from one stable state to the other propagates along the chain and excites a complex system of waves. In the first part of the paper ( Cherkaev et al., 2004, Transition waves in bistable structures. I. Delocalization of damage), the branches could be separated by a gap where the tensile force is zero, the transition wave was treated as a wave of partial damage. Here we assume that there is no zero-force gap between the branches. This allows us to obtain steady-state analytical solutions for a general piecewise linear trimeric diagram with parallel and nonparallel branches and an arbitrary jump at the transition. We derive necessary conditions for the existence of the transition waves and compute the speed of the wave. We also determine the energy of dissipation which can be significantly increased in a structure characterized by a nonlinear discontinuous constitutive relation. The considered chain model reveals some phenomena typical for waves of failure or crushing in constructions and materials under collision, waves in a structure specially designed as a dynamic energy absorber and waves of phase transitions in artificial and natural passive and active systems.

Transition waves in bistable structures. I. Delocalization of damage

We consider chains of dimensionless masses connected by breakable bistable links. A non-monotonic piecewise linear constitutive relation for each link consists of two stable branches separated by a gap of zero resistance. Mechanically, this model can be envisioned as a ”twin-element” structure which consists of two links (rods or strands) of different lengths joined by the ends. The longer link does not resist to the loading until the shorter link breaks. We call this construction the waiting link structure. We show that the chain of such strongly non-linear elements has an increased in-the-large stability under extension in comparison with a conventional chain, and can absorb a large amount of energy. This is achieved by two reasons. One is an increase of dissipation in the form of high-frequency waves transferring the mechanical energy to heat; this is a manifestation of the inner instabilities of the bonds. The other is delocalization of the damage of the chain. The increased stability is a consequence of the distribution of a partial damage over a large volume of the body instead of its localization, as in the case of a single neck formation in a conventional chain. We optimize parameters of the structure in order to improve its resistance to a slow loading and show that it can be increased significantly by delocalizing a damage process. In particular, we show that the dissipation is a function of the gap between the stable branches and find an optimal gap corresponding to maximum energy consumption under quasi-static extension. The results of numerical simulations of the dynamic behavior of bistable chains show that these chains can withstand without breaking the force which is several times larger than the force sustained by a conventional chain. The formulation and results are also related to the modelling of compressive destruction of a porous material or a frame construction which can be described by a two-branched diagram with a large gap between the branches. We also consider an extension of the model to multi-link chain that could imitate plastic behavior of material.

Quasi-static and dynamic mechanical response of Strombus gigas (conch) shells

Quasi-static and dynamic compression and three-point bending tests have been carried out on Strombus gigas (conch) shells. The mechanical response is correlated with its microstructure and damage mechanisms. The mechanical response is found to vary significantly from specimen to specimen and requires the application of Weibull statistics in order to be quantitatively evaluated. The conch exhibited orientation dependence of strength as well as significant strain-rate sensitivity; the failure strength at loading rates between 10×10 3 and 25×10 3 GPa s −1 was approximately 50% higher than the quasi-static strength. Quasi-static compressive failure occurred gradually, in a mode sometimes described as ‘graceful failure’. Crack deflection, delocalization of damage, and viscoplastic deformation of the organic layers are the most important mechanisms contributing to the unique mechanical properties of these shells.

Knitted composites for energy absorption under tensile loading

Abstract A new class of knitted composites has been designed to maximize the total energy absorbed during tensile failure. Knitted loops of light, continuous fiber tows are configured in such a way that they must be drawn through relatively large displacements before they come into direct contact with one another. Upon loop contact, the material hardens locally, forcing further damage to develop by the same process elsewhere. In this way the entire gauge section absorbs energy before ultimate failure. Levels of energy absorption per unit volume reach 40 MJ/m 3 and, per unit mass, 25 J/g. The mechanisms involved in damage delocalization and failure are detailed and modeled in a simple manner. While the current values of energy absorption are already attractive, the models indicate that much higher values could be attained with optimized composites.

Quasi-static and dynamic mechanical response of Haliotis rufescens (abalone) shells

Quasi-static and dynamic compression and three-point bending tests have been carried out on Haliotis rufescens (abalone) shells. The mechanical response of the abalone shell is correlated with its microstructure and damage mechanisms. The mechanical response is found to vary significantly from specimen to specimen and requires the application of Weibull statistics in order to be quantitatively evaluated. The abalone shell exhibited orientation dependence of strength, as well as significant strain-rate sensitivity; the failure strength at loading rates between 10×10 3 and 25×10 3 GPa/s was approx. 50% higher than the quasi-static strength. The compressive strength when loaded perpendicular to the shell surface was approx. 50% higher than parallel to the shell surface. The compressive strength of abalone is 1.5–3 times the tensile strength (as determined from flexural tests), in contrast with monolithic ceramics, for which the compressive strength is typically an order-of-magnitude greater than the tensile strength. Quasi-static compressive failure occurred gradually, in a mode sometimes described as “graceful failure”. The shear strength of the organic/ceramic interfaces was determined to be approx. 30 MPa by means of a shear test. Considerable inelastic deformation of the organic layers (up to a shear strain of 0.4) preceded failure. Crack deflection, delocalization of damage, plastic microbuckling (kinking), and viscoplastic deformation of the organic layers are the most important mechanisms contributing to the unique mechanical properties of this shell. The plastic microbuckling is analysed in terms of the equations proposed by Argon ( Treatise of Materials Science and Technology. Academic Press, New York, 1972, p. 79) and Budiansky ( Comput. Struct. 1983, 16, 3).

Lockup, chains and the delocalization of damage

Whether damage is localized or delocalized in a composite, the composite's fracture toughness when localization occurs can be controlled to a much greater extent than hitherto exploited by properly choosing the composite's internal geometry. Delocalization and high toughness are both favoured by building in systematic defects and lock-up mechanisms. Widespread defects make available arbitrarily many sites at which energy may be absorbed by non-linear behaviour. Lock-up mechanisms cause local hardening following local damage, which drives subsequent damage to initiate elsewhere, possibly leading to damage delocalization. In brittle-brittle composites, these mechanisms may be the best hope for achieving toughness values similar to those of alloys. Illustrations are taken from recent research into woven composites with three-dimensional reinforcement and new work on model composites.