International Journal of Fracture最新文献

To improve the fatigue performance of laser-welded TC4 titanium alloy joints, ultrasonic rolling processing (USRP) is employed herein. Multiple passes of USRP (viz., one, three, and five) are conducted using an ultrasonic rolling device. Results reveal that USRP considerably improves the fatigue limit and life of the welded joints. At room temperature, the fatigue strength of the weldment increases by 2.04–4.58% and the corrosion fatigue life increases by 1.72–2.88 times. In addition, to reveal its strengthening mechanism, the effects of USRP on the surface morphology, microstructure, surface residual stress, and microhardness of the laser-welded TC4 titanium alloy joints are investigated. USRP leads to a shift in the crack initiation point to the subsurface and formation of a hardened layer with high residual stress on the surface via the application of considerable static pressure input and multiple passes. Consequently, fatigue striations become narrower and denser. Compared to the traditional weld surface treatment, USRP substantially improves the surface quality and fatigue performance of laser-welded TC4 titanium alloy joints.

In this expository Note, it is shown that the Griffith phase-field theory of fracture accounting for material strength originally introduced by Kumar, Francfort, and Lopez-Pamies (J Mech Phys Solids 112, 523–551, 2018) in the form of PDEs can be recast as a variational theory. In particular, the solution pair ((textbf{u},v)) defined by the PDEs for the displacement field (textbf{u}) and the phase field v is shown to correspond to the fields that minimize separately two different functionals, much like the solution pair ((textbf{u},v)) defined by the original phase-field theory of fracture without material strength implemented in terms of alternating minimization. The merits of formulating a complete theory of fracture nucleation and propagation via such a variational approach — in terms of the minimization of two different functionals — are discussed.

Phase-field models of brittle fracture are typically endowed with a decomposition of the elastic strain energy density in order to realistically describe fracture under multi-axial stress states. In this contribution, we identify the essential requirements for this decomposition to correctly describe both nucleation and propagation of cracks. Discussing the evolution of the elastic domains in the strain and stress spaces as damage evolves, we highlight the links between the nucleation and propagation conditions and the modulation of the elastic energy with the phase-field variable. In light of the identified requirements, we review some of the existing energy decompositions, showcasing their merits and limitations, and conclude that none of them is able to fulfil all requirements. As a partial remedy to this outcome, we propose a new energy decomposition, denoted as star-convex model, which involves a minimal modification of the volumetric-deviatoric decomposition. Predictions of the star-convex model are compared with those of the existing models with different numerical tests encompassing both nucleation and propagation.

Mesh size dependency caused by strain localization is an ongoing problem in numerical simulations using the finite element method. In order to solve this problem, the concept of including the characteristic element length for regularization is used in the literature. The estimation of the characteristic element length is not a straightforward task since normally the characteristic element length differs from one element to another in the simulation and depends not only on element geometry but also on fracture plane orientation and material orientation. In this paper, an innovative method is proposed to estimate the characteristic element length which works on the orthogonal projection of elements on the fracture plane. The method is implemented in Abaqus/Explicit finite element solver and is verified using simple and more complex load cases such as tensile specimens, open hole specimens, and low-velocity impact. A good correlation between the numerical and experimental results in all of the studied cases was achieved and the proposed method proved to be effective in reducing mesh sensitivity. The use of the volumetric method from the literature for the simulation of open-hole tensile specimens led to more than 25% increase in the estimation of specimen strength while similar values of strength for different element aspect ratios were achieved with the proposed method.

An energy-based analytical model is proposed here to investigate the mechanical behavior of adhesively bonded simple-lap and stepped-lap joints (SLJ) with carbon fiber-reinforced polymer (CFRP) adherends subjected to tensile loading. In this study, the CFRP uni-directional (UD) adherends of ([0]_{16}) and quasi-isotropic (QI) layup sequence of ([45/-45/0/90]_{2s}) are considered to be joined. The governing differential equations (GDEs) of equilibrium are derived for the adhesively bonded adherends in stepped lap joint configuration following an energy-based approach. Additionally, this model is reduced for GDEs of the simple-lap joint configuration. The finite difference scheme is employed to obtain the numerical solution of the proposed analytical model. The field distributions of strain and displacement over the specimen surfaces are captured in the experimental investigation using the full field technique of 2D digital image correlation (DIC). The analytical model generates the load–displacement curve, validated against experimental and finite element (FE) predictions. Additionally, a sensitivity analysis is conducted to assess the influence of the design parameters of the adhesive joint, including the thickness of the adhesive layer, length of overlap region, and elastic modulus. Finally, the analytical model prediction of the peak load for damage in adhesively bonded joints under shear loading is compared with experimental results. The developed analytical model provides an understanding of the mechanical behavior, including possible failure/critical locations of the adhesive joints from the design perspective.

The fatigue crack growth behavior of a submicron-grained WC–Co hardmetal is investigated by artificially introducing small flaws by means of sharp indentation. Similar fatigue testing is also conducted on notched specimens with long through-thickness cracks for comparison purposes. The use of controlled small indentations flaws is shown to be a valid and successful approach for studying and describing crack growth behavior under cyclic loading for the material under consideration. This statement is based on the similitude found in fatigue mechanics and mechanisms between both crack types. Regarding the former, accounting of the indentation-induced residual stresses is key to rationalize the experimental findings. Concerning the latter, inspection of crack-microstructure interaction as well as fracture surfaces permit to discern similar features and scenarios, at both meso- and micrometric length scales. Results from this research yield an immediate practical implication, as indentation techniques may then be proposed as an alternative testing route for investigating fatigue crack growth behavior of hardmetal grades where sharp indentation is capable to induce well-developed radial crack systems.

Contrary to the second-order Phase field model (PFM) of fracture, fourth-order PFM provides a more precise representation of the crack surface by incorporating higher-order derivatives (curvature) of the phase-field order parameter in the so-called crack density functional. As a result, in a finite element setting, the weak form of the phase-field governing differential equation requires (C^1) continuity in the basis function. (C^0) Sibson interpolants or Natural element interpolants are obtained by the ratio of area traced by the second-order Voronoi cell over the first-order Voronoi cells, which is based on the natural neighbor of a nodal point set. (C^1) Sibson interpolants are obtained by degree elevating the evaluated (C^0) interpolants in the Bernstein-Bezier patch of a cubic simplex. For better computational efficiency while accounting only for the tensile part for driving fracture, a hybrid PFM is adopted. In this work, the numerical implementation of higher-order PFM with (C^1) Sibson interpolants along with some benchmark examples are presented to showcase the performance of this method for simulating fracture in brittle materials.

This work examines the void growth and coalescence in isotropic porous elastoplastic solids with sigmoidal material hardening via finite element three-dimensional unit cell calculations. The investigations are carried out for various combinations of stress triaxiality ratio (({mathcal {T}})) and Lode parameter (({mathcal {L}})) and consider a wide range of sigmoidal hardening behaviors with nominal hardening rates spanning two decades. The effect of ({mathcal {L}}) is considered in the presence and in the absence of imposed shear stress. Our findings reveal that depending on the nature of sigmoidal hardening the cell stress-strain responses may exhibit two distinct transitions with increasing stress triaxiality (({mathcal {T}})). Below a certain lower threshold triaxiality the stress-strain responses are sigmoidal, while above a certain higher triaxiality they exhibit softening immediately following the yield. Between these threshold levels, the responses exhibit an apparent classical rather than sigmoidal strain hardening. The sigmoidal hardening characteristics also influence porosity evolution, which may stagnate before a runaway growth up to final failure. For a given ({mathcal {L}}), an imposed shear stress adversely affects the material ductility at moderate ({mathcal {T}}) whereas at high ({mathcal {T}}) it improves the ductility. Finally, we discuss the role of material hardening and stress state on the residual cell ductility defined as strain to final failure beyond the onset of coalescence.

The present study investigates in the failure of adhesive bondings with structural silicone sealants. Point connectors of two circular metal adherends bonded with DOWSIL™ TSSA are subjected to tensile loading. We formulate and use a constitutive law that captures volumetric softening owing to the formation of cavities. Therein, cavitation is considered a process of elastic instability which is homogenized with a pseudo-elastic approach. Ultimate failure initiating from the free edges is predicted employing the framework of finite fracture mechanics. The concept requires both a strength-of-materials condition and a fracture mechanics condition to be satisfied simultaneously for crack nucleation. For the former, we use a novel multiaxial equivalent strain criterion. For the latter, we employ literature values of the fracture toughness of DOWSIL™ TSSA . The predicted onset of cavitation and ultimate failure loads are in good agreement with our experiments. The proposed model provides initial crack lengths that allow for the derivation of simple engineering models for both initial designs and proof of structural integrity while simultaneously extending the range of usability of the structural silicone compared to standardized approaches.