Documents published in Scipedia

• Multiscale modeling of hydrogen transport in steels and its resulting embrittlement effect

  X. Gao, G. Rao, C. Huang

  WCCM2024.

  
  

  Abstract

  A multiscale modeling approach is adopted in this study to understand the hydrogen embrittlement (HE) mechanisms and to predict failure of engineering components under the influence of hydrogen environment. Molecular dynamics simulations of the bodycentered cubic (BCC) iron are conducted to examine the theories of hydrogen enhanced localized plasticity (HELP) and hydrogen enhanced decohesion (HEDE). It is shown that hydrogen aggregation at the crack tip and along grain boundary (GB) reduces the surface energy for creating new crack surfaces, leading to changes in fracture modes caused by preemptive crack propagation. At the continuum level, a numerical framework is developed, which incorporates hydrogen transport in steels and the resulting HELP and HEDE mechanisms into a finite element phase field model to predict crack initiation and propagation in engineering components. As an example, a compact tension (CT) specimen made of a pipeline steel is analyzed. The numerical model captures the phenomenon of hydrogen aggregation occurring proximal to the crack tip driven by the high gradient of hydrostatic stress and large plastic deformation in this region. The resultant hydrogen concentration elicits an interplay of HELP and HEDE effects and reduces the specimen’s load carrying capacity. With properly chosen model parameters, the numerical model has the potential of serving as tool for predicting crack propagation and ductile to brittle transition due to the presence of hydrogen.

  Abstract
  A multiscale modeling approach is adopted in this study to understand the hydrogen embrittlement (HE) mechanisms and to predict failure of engineering components under the [...]

  • 0
  •  read

• Critical planes analysis of the impact of porosities on the fatigue of metal solids

  F. Fauvin, E. Feulvarch, G. Debono

  WCCM2024.

  
  

  Abstract

  In this work, we take interest in the impact of defects present in metal solids manufactured by material fusion or by additive manufacturing on their fatigue life during cyclic loading. Indeed, we observe a more or less strong local plasticity around the defects even if the stresses remain below the elastic limit, which can strongly impact the fatigue life of such solids. In the case of a part obtained by steel casting, it is the retassures that make the part most vulnerable. In the case of solids obtained by additive manufacturing, the most damaging defects are surface roughness and porosities linked to a lack of fusion. In order to estimate the fatigue life of such solids, it is necessary to observe the states of stress and strain around the defects during a cycle. As stress levels can be relatively high locally, critical plane type criteria are relevant for estimating the fatigue life of such solids. In order to carry out a fatigue analysis of a part obtained by steel casting or by additive manufacturing, we propose to model it by finite elements, with a refinement of the elements around the porosities, then to calculate the local stress and strain states, and finally to implement a critical plane type criterion, like the Fatemi-Socie criterion. The critical planes are the planes on which the maximal shear strain amplitudes occur. The local stress and strain states can be highly multi-axial. So the determination of the critical planes can be very computationally and storage consuming. In the present work, an analysis in the space of deviators of the deformation tensor makes possible determination of such planes in each of the numerous nodes of the mesh. These three steps of calculation, correlated with experimental tests, makes it possible to envisage obtaining fatigue life laws for numerous metallic materials presenting defects.

  Abstract
  In this work, we take interest in the impact of defects present in metal solids manufactured by material fusion or by additive manufacturing on their fatigue life during cyclic [...]

  • 0
  •  read

• Semi-analytical failure prediction of adhesive joints by Finite Fracture Mechanics

  T. Methfessel, C. El Yaakoubi-Mesbah, W. Becker

  WCCM2024.

  
  

  Abstract

  The current contribution suggests a semi-analytical structural model for an adhesive joint with a closed-form higher-order description of the adhesive layer and the potential occurrence of a debonding crack. This enables a highly efficient failure prediction by the concept of Finite Fracture Mechanics, employing a coupled failure criterion that consists of a stress and an energy subcriterion. The comparison with accompanying finite element calculations and experimental findings demonstrates the high predictive quality of this approach

  Abstract
  The current contribution suggests a semi-analytical structural model for an adhesive joint with a closed-form higher-order description of the adhesive layer and the potential [...]

  • 0
  •  read

• Fatigue crack propagation behavior analysis of 15MnTi steel based on cyclic cohesion model

  J. Guo, J. He, X. Sun

  WCCM2024.

  
  

  Abstract

  15MnTi steel is widely used in high load structures such as bridges, pressure vessels, ships, and vehicles due to its excellent mechanical properties. In the course of service, the failure of steel structure is mostly caused by fatigue fracture. In order to investigate the crack growth of 15MnTi steel under fatigue load, the cohesive zone model (CZM) was used to simulate the crack growth. The CZM can simulate brittle and plastic fracture behavior by using the function of crack interface opening force and opening displacement to avoid the stress singularity of crack tip. On this basis, a cyclic cohesive zone model (CCZM) was established to study the fatigue crack propagation behavior. This model effectively links damage, tractive force, and cumulative displacement while incorporating the process of fatigue crack growth to accurately simulate material damage evolution under fatigue load. Experimental studies on crack growth in 15MnTi steel at three stress ratios reveal a linear relationship between crack growth rate and stress intensity factor range for different stress ratios. The parameters of Paris formula were calculated using crack growth rate and stress intensity factor range, which provided reference for the selection of model parameters. By utilizing the user element subroutine (UEL) in Abaqus and compiling the CCZM using Fortran language specifically for 15MnTi steel, simulations were conducted to analyze the evolution of crack tip state under various stress ratios and discuss the corresponding crack growth behavior based on experimental observations. The results demonstrate that the fatigue crack propagation rate varies linearly with both stress ratio range and stress intensity factor range, consistent with experimental findings. The results of the opening and closing evolution of the crack tip are consistent with the law of crack propagation, which indicates that the plastic behavior of the crack tip can be effectively characterized by the CCZM. Furthermore, parameters obtained from the cyclic cohesive zone model's Paris formula closely match experimental data, thus validating its accuracy and feasibility in simulating fatigue crack propagation behavior.

  Abstract
  15MnTi steel is widely used in high load structures such as bridges, pressure vessels, ships, and vehicles due to its excellent mechanical properties. In the course of service, [...]

  • 0
  •  read

• Numerical simulation of the swelling and deswelling process of gel

  I. Riku, K. Mimura

  WCCM2024.

  
  

  Abstract

  It is well known that the entropy elasticity of rubberlike materials and Brownian motion are described by formally analogous equations as both originated from thermal fluctuations. In rubberlike materials, the shear modulus is conventionally considered to be proportional to the absolute temperature and the proportionality factor is the number density of polymer chains for an affine polymer chains’ network model. On the other hand, the self-diffusion coefficient of Brownian motion is described as the product of the mobility and the absolute temperature. However, for the polymer chains’ network in a solvent, the interaction between the polymer chains and the solvent molecules occurs and the collective diffusion coefficient of the solvent molecules should be different to the self-diffusion coefficient of Brownian motion. Moreover, the shear modulus of the resultant polymer gel should be dependent on the swelling ratio due to the nonaffine movement of polymer chains. Therefore, to verify the analogy of the equations for the shear modulus of the nonaffine polymer chains’ network model and the collective diffusion coefficient of the solvent molecules, in this study, the swelling and deswelling process of the polymer gel is investigated by the numerical simulations.

  Abstract
  It is well known that the entropy elasticity of rubberlike materials and Brownian motion are described by formally analogous equations as both originated from thermal fluctuations. [...]

  • 0
  •  read

• Numerical studies of compression failure in triply periodic minimal surface-based ceramic foams

  T. Tran, R. Piat

  WCCM2024.

  
  

  Abstract

  Microstructures with minimal surfaces can be often found in natural porous architectures, where the surface tension minimizes the area. The triply periodic minimal surfaces (TPMS) [1] are an example of such microstructures. Compared with other porous structures, TPMS have three significant features: firstly, their geometries can be completely expressed via analytical functions; secondly, TPMS are periodic in three independent directions and thirdly, the mean curvature of TPMS is zero [2]. Transforming the TPMS-based unit cell into a lattice structure has particular usage in aerospace, nuclear energy, and biomedical applications where light weight, high stiffness, and temperature resistance are of critical importance. In the presented studies, the failure behavior of four typical TPMS structures (Primitive, Gyroid, Neovius, and IWP) under compression was studied using finite element analysis. Numerical modeling of the damage propagation and strength prediction was performed by removing the finite elements in which the appropriate damage criterion is reached. Utilizing the equations of the generated TPMS structures, the wall thickness of unit cell was considered the main parameter that defined the ceramics volume fraction and should be taken into consideration. Therefore, various unit cell models for different wall thicknesses were generated and used to investigate the impact of the cell geometry on the damage initiation, propagation, and overall compression strength. The results of compression strength and damage development were compared with those of other TPMS structures for the same wall thickness and volume fraction. Finally, the grade TPMS porous structure was provided to verify the effect of wall thickness variation on damage evolution on the macroscale.

  Abstract
  Microstructures with minimal surfaces can be often found in natural porous architectures, where the surface tension minimizes the area. The triply periodic minimal surfaces [...]

  • 0
  •  read

• Penetration resistance of graphene coated ceramic materials under projectile impacts

  M. Talebi Bidhendi, K. Behdinan

  WCCM2024.

  
  

  Abstract

  Extreme conditions including impact can result in material degradation, permanent damages, and occasionally property/life loss. Therefore, investigation of materials and structures under projectile impact has been a canonical field of research over the past decades. Such studies have led to the development of hybrid materials with high performance and durability under the aforementioned loading. As an emerging hybrid material, graphene oxide (GO) - silicon carbide (SiC) provides promising thermo-chemo-mechanical properties with various applications in defense, energy, and aerospace engineering. Nevertheless, penetration resistance of such composites under impact received less attention due to experimental and computational difficulties. Here, ReaxFF molecular dynamics is leveraged to address the aforesaid problem around room temperature. In that regard, the response of 4H-SiC thin films coated by GO samples under indentation and high-velocity projectile impact is studied. It is observed that (a) ceramic substrates coated by GO samples with higher functional groups concentration (oxidation degree) demonstrate softer behavior under indentation, and (b) fracture and penetration resistance under high-velocity impact are altered based on the oxidation degree of the coating layers. In essence, impact-induced complete perforation becomes more localized to the impacted region by increasing the oxidation content of the coating layers. The influence of oxygen functional groups on the adhesion energy between GO and SiC layers is also investigated. It is observed that adhesion energy between SiC and the coating can be ameliorated by the oxidation degree of the graphene samples. Eventually, the above-mentioned findings provide some insights into the bottom-up design pathways for developing ceramic-based protective barriers in which GO is used as a coating layer or reinforcement

  Abstract
  Extreme conditions including impact can result in material degradation, permanent damages, and occasionally property/life loss. Therefore, investigation of materials and structures [...]

  • 0
  •  read

• A primal hybrid finite element method to solve general compressible, quasi-incompressible and incompressible elasticity using stable H(div)-L2 spaces

  P. Devloo, G. Avancini, N. Shauer, H. Oliveira

  WCCM2024.

  
  

  Abstract

  Hybrid methods are usually derived from an extended variational principle, in which the interelement continuity of the functions subspace is removed and weakly enforced by means of a Lagrange multiplier. In this context, a new primal hybrid finite element formulation is presented, which uses H(div) conforming displacement functions and discontinuos L2 approximation for pressure together with shear traction functions to weakly enforce tangential displacement. This combination allows the simulation of compressible, quasi-incompressible and fully incompressible elastic solids, with convergence rates independent of its bulk modulus. The proposed approach benefits from the property that the divergence of the H(div) displacement functions is De Rham compatible with the (dual) pressure functions. The hybridization of the tangential displacements is weakly enforced through a lower order shear stress space. This leads to a saddle-point problem that is stable over the full range of poisson coefficient (large compressibility up to incompressible). Moreover, a boundary stress (normal and shear) can be recovered that satisfies elementwise equilibrium. Hybridizing the tangent stresses and condensing the internal degrees of freedom, a positive-definite matrix with improved spectral properties can be recovered. The stability, consistency and local conservation features are discussed in details. The formulation is tested and verified for different test cases.

  Abstract
  Hybrid methods are usually derived from an extended variational principle, in which the interelement continuity of the functions subspace is removed and weakly enforced by [...]

  • 0
  •  read

• Complete variable kinematic cuf-based multilayered shell elements

  E. Carrera, D. Scano

  WCCM2024.

  
  

  Abstract

  The paper presents a methodology for formulating multi-layered composite shell theories with arbitrary kinematic fields. Each displacement variable is examined through an independent expansion function, allowing integration of equivalent single layer and layer-wise approaches within the Carrera Unified Formulation. Finite element method discretizes the structure in the reference plane of the plate using Lagrange-based elements. Governing equations are derived using the principle of virtual displacements. The study considers multilayered structures with different radius-to-thickness ratios and compares results with analytical solutions from the literature. Findings suggest the most appropriate model selection depends strongly on specific problem parameters

  Abstract
  The paper presents a methodology for formulating multi-layered composite shell theories with arbitrary kinematic fields. Each displacement variable is examined through an [...]

  • 0
  •  read

• Band gap evolution in nonlinear dynamics of metamaterials made structures via gradually-changing mechanical properties

  R. Augello, E. Carrera

  WCCM2024.

  
  

  Abstract

  This paper explores the dynamic behavior of metamaterial-like structures by investigating the evolution of their band gap under the influence of geometrical nonlinearities in the large displacement/rotations field. The study employs a unified framework based on the Carrera Unified Formulation (CUF) and a total Lagrangian approach to develop higher-order onedimensional beam theories that account for geometric nonlinearities. The axis discretization is achieved through a finite element approximation. The equations of motion are solved around nonlinear static equilibrium states, which are determined using a Newton–Raphson algorithm combined with a path-following method of arc-length type. The CUF approach introduces two key innovations that are highly suitable for the evolution of the band gap: 1) Thin-walled structures can be effectively represented using a single one-dimensional beam model, overcoming the common limitations of standard finite elements. This is crucial as three-dimensional solid elements would result in significant computational costs, and twodimensional elements pose limitations for this type of investigation. Finally, employing onedimensional finite elements usually requires a combination of elements, leading to additional mathematical complexities in their connections and lacking geometric precision. 2) CUF enables the use of the full Green-Lagrange strain tensor without the need for assumptions, as is the case with von Karm´ an nonlinearities. ´ The paper specifically compares results obtained with linear and nonlinear stiffness matrices, highlighting the differences. Numerical investigations are conducted on thin-walled structures composed of repeatable cells, assessing mode changes under traction and compression loading. The findings emphasize that the band gap is an inherent property of the equilibrium state, underscoring the necessity of a proper nonlinear analysis for accurately evaluating frequency transitions

  Abstract
  This paper explores the dynamic behavior of metamaterial-like structures by investigating the evolution of their band gap under the influence of geometrical nonlinearities [...]

  • 0
  •  read