In-plane Loading Conditions Research Articles

A novel elastoplastic constitutive model for woven oxide/oxide ceramic matrix composites with anisotropic hardening

The oxide/oxide ceramic matrix composite exhibits superior mechanical properties in high temperature environment. However, complex nonlinear behavior is not clarified for high performance applications. The present work developed an elastoplastic constitutive model considering variations of hardening behavior over the stress states by introducing a novel loading function. The model can account for heterogeneous initial yield and complex hardening behavior accurately and was verified from experiments under tension and compression conditions with various off-axis angles. The computational results agree with stress-strain responses containing softening up to failure under arbitrary in-plane loading conditions.

Stress distribution along the cruciform geometry under pure in-plane biaxial loading condition

The present paper aims at designing a novel cruciform geometry which could effectively demonstrate the biaxial behavior of aluminum A1050-H14. A cruciform geometry with two geometric shapes milled about the center region on the basic cross-shaped geometry is considered for the present study. The geometric shapes include a double-armed cruciform and a circle but with different depths (geometric-shaped CS-I). An FEA tool is used to study the biaxial behavior of these geometries under two biaxial loading conditions: (1) biaxial tension (TT) and (2) biaxial compression–tension (CT). Along with the above-mentioned geometry, two more geometries are even analyzed to end up with a better geometry for the in-plane biaxial testing. The other two geometries are (1) modified cruciform with spline cut at the cross-arms of the sample and with a straight arm (CS-II), and (2) modified CS-I geometry by tapering the arms (CS-III). The geometry producing (1) uniform von Mises stress, (2) zero or minimal shear stress along the gauge section and (3) initiation of failure about the gauge section is considered.

Failure and complex crack patterns in hybrid laminates: A phase-field approach

A powerful numerical instrument, which reproduces the complex failure mechanisms of hybrid laminates under in-plane loading conditions, is developed within the framework of phase-field modelling. The ruptures, strongly influenced by geometrical and mechanical properties of the plies and affected by the state of stress, are arranged as delamination of the adhesive interface and intricate crack patterns within the layers. Therefore, the mechanical response of a hybrid laminate is obtained by studying the simplified layup of two elastic-brittle solids connected by a cohesive interface. Explicit and well detailed simulations illustrate peculiar failure mechanisms, validated, when possible, against experimental results taken from the literature and compared to simplified analytical models. Different in-plane loading conditions are explored together with the possibility to include material anisotropy. The proposed model is a first attempt to provide an effective design tool for the understanding of the intriguing failure of hybrid laminates and the enhancement of their mechanical properties like ductility.

A semi-empirical modeling approach for predicting the deformational capacity of axially-compressed cylindrical shells based on a novel material stress-strain characterization method

Adoption of cylindrical shell structures for various load-resistance applications has enjoyed wide-spread acceptance in the field of civil, mechanical and aerospace engineering, mainly due to the exceptional structural efficiency of cylindrical shells to withstand significant longitudinal and circumferential in-plane loading without bending. However, where such in-plane loading conditions are compressive, cylindrical shells are likely to exhibit an unstable response characterized by localized out-of-plane deformation. Computerized numerical simulation is often required for accurate and efficient estimation of the strains and resultant stresses in cylindrical shells under loading, especially where the thickness of the shell is sufficient to evoke an inelastic buckling response in the structure. The buckling behavior of thin-walled cylindrical shells subjected to uniform axial compression has been studied in this paper using the finite element (FE) simulation method to assign respective material, geometric, loading and boundary properties to computer-generated cylindrical shell specimens. Extensive parametric analysis, consisting of approximately 720 FE runs, was then conducted based on a full-factorial empirical design, applying ample variations of the relevant parameters that influence the buckling response of axially-compressed cylindrical-shell structures. Nonlinear multiple regression techniques were then employed to derive the coefficients of nonlinear mathematical expressions, each developed as an arithmetic product of appropriate variable functions related to the respective functional sensitivities of the investigated parameters. Strain-hardening properties were incorporated into the mathematical expressions based on the shape constants of the Ndubuaku stress-strain model; which has proven to be remarkably useful for accurate parameterization of the stress-strain behavior over the full range of strains for a wide range of metallic materials, including materials with a well-defined yield plateau. Excellent predictions of FEA-derived values for the critical limit strain limit were obtained, and a simple statistical approach was presented to increase the conservativeness of the semi-empirical model as required.

Electro-mechanical characterization of three-dimensionally conductive graphite/epoxy composites under tensile and shear loading

Abstract An experimental study was performed to compare the electro-mechanical response of three-dimensionally conductive woven carbon fiber/epoxy laminated composites under quasi-static uniaxial tensile and in-plane shear loading conditions. Three-dimensional (3D) electrical network was generated in these composites by embedding carbon nanotubes (CNTs) of 0.025 wt% in the epoxy and reinforcing short carbon fibers (150 μm and 350 μm long) with a fiber density of 1000 fibers/mm2 between the laminates using electro-flocking process. CNTs are effectively dispersed in the epoxy matrix using a combination of ultrasonication and shear mixing techniques. A compression molding fabrication technique was employed to fabricate composite materials. For all composite types, in general, the in-situ electrical response showed a trend of initial decrease in resistance and later increase in resistance for tensile loading. However, no noticeable increase in electrical resistance was observed until failure of the composite under shear loading conditions. Both CNTs and short carbon fibers made new contacts with neighboring carbon fiber laminates for entire duration of shear loading even though the composite was undergoing progressive failure.

Constitutive models for anisotropic dielectric elastomer composites: Finite deformation response and instabilities

This paper is concerned with the generation of homogenization estimates for electroelastic composites consisting of initially aligned, rigid dielectric fibers that are distributed with random positions in a dielectric elastomeric matrix. For this purpose, use is made of a certain “partial decoupling strategy” resulting in the splitting of the macroscopic energy of the composite into a purely mechanical and a purely electrostatic component—coupled only by the average rotation of the fibers. In addition to the macroscopic electro-mechanical constitutive response for the composite, the procedure delivers estimates for the average fiber rotation as a consequence of the combined action of the mechanical stresses and electrical torques under general in-plane loading conditions. It is found that when large compressive stresses are applied along the long axes of the fibers, the composite may undergo a “macroscopic” (i.e., material) instability that is captured by loss of ellipticity of the overall incremental response and corresponds to spontaneous rotation of the fibers to relieve the large stresses. Moreover, when the electric field is aligned with the long axes of the fibers, it tends to stabilize the response, while when it is transverse to them, it tends to destabilize the response. Earlier estimates obtained by means of a simplifying “partial decoupling approximation” are compared with the new, more robust estimates and found to become less accurate with increasing electric field magnitudes.

Experimental and numerical investigations of cross-laminated timber elements at in-plane beam loading conditions

Abstract Cross laminated timber (CLT) at in-plane beam loading conditions presents a complex stress state wherefore several failure modes and geometry parameters need to be considered in design. The work presented here includes experimental investigations of CLT beams for comparison and validation of an analytical model and design proposals previously suggested by the authors. All relevant failure modes are considered; bending failure and shear failure modes I, II and III. The main focus is, however, on shear failure mode III relating to shear failure in the crossing areas between orthogonally bonded longitudinal and transversal lamination. The analytical model presented is an improvement of the analytical model which has been suggested to be used as the basis for design equations for the next version of Eurocode 5. The two design proposals presented are based on that improved analytical model. Experimental results show good agreement with the improved model and both design proposals. In order to study the influence of different lamination placements and varying lamination widths, comparisons between the improved analytical model and FE-analyses regarding magnitude and distribution of internal forces are presented and good agreement is obtained. Experimental and analytical results indicate only a small influence of reduced lamination widths close to the beam edges. This is a finding which is of practical interest since CLT beams in general are cut from larger elements, with no consideration of the location of the individual laminations with respect to the edges of the beam.

Crushing behavior of honeycomb structure: a review

This article concludes some of the important observation regarding quasi-static and dynamic crushing response of honeycomb structure carried out by authors and addressed in the literature. The behaviour of honeycomb structure has been reported through experimentation, mathematical and numerical models. The influence of cell wall thickness, node length, cell size and loading has been studied in detail leading to some important findings which have not been addressed earlier. The crushing responses of honeycomb structure have been studied in both out-of-plane and in-plane loading condition. Moreover, its bending behaviour has also been reported in few studies. Geometrical core configuration and geometric property like cell size, cell wall thickness and node length etc. play a defining role in administrating potential of honeycomb. Relative density was a vital property of honeycomb dependent on cell configuration and geometric properties. Facesheet material and thickness majorly effects the energy absorption capability of the core during dynamic projectile and impulsive impacts.

Modeling the transverse tensile and compressive failure behavior of triaxially braided composites

The complex failure behavior of triaxially braided composites under in-plane transverse load conditions is investigated through quasi-static experiments and meso-scale finite element (FE) simulations. A three-dimensional (3D) progressive damage model for the fiber tows is integrated with a cohesive model for the interfaces to simulate the initiation, accumulation and propagation behavior of damage in braided composites. The meso-scale FE model predicts well the global stress–strain responses, and the predicted strain distribution contours compare well with the experimental results captured by digital image correlation. The fully validated FE model is subsequently adopted to investigate the failure mechanism of a triaxially braided composite under transverse tensile and compressive loads. Numerical parametric studies are implemented to evaluate the effect of interface strength on the effective properties of the material and to identify the appropriate definition of through-thickness boundary conditions in the meso-FE simulation. The model presented in this study shows fairly good accuracy in predicting the failure behavior of a triaxially braided composite under different loadings, and it can be further employed to study the mechanical performance of similar materials.

Cross laminated timber at in-plane beam loading – Comparison of model predictions and FE-analyses

The work presented concerns validation of a specific analytical model for Cross Laminated Timber (CLT) at in-plane beam loading conditions. The original model (model A) has previously been presented in the literature and is also suggested to be used as a basis for design equations for the next version of Eurocode 5. An improved version (model B) of that original model (model A), regarding basic assumptions relating to the internal force distribution, has recently been presented in the literature. Here, comparisons between the original model (model A), the improved model (model B) and FE-analyses regarding magnitude and distribution of internal forces are presented. The main focus is on forces and torsional moments acting in the crossing areas between longitudinal and transversal laminations and relevant for shear mode III failure, meaning the relative sliding and rotation between two flat-side bonded laminations. The results show that the improved analytical model (model B) outperforms the original model (model A) in terms of giving predictions very close to the predictions of the FE-model. A further extension of the improved model (model B) regarding distribution of forces and torsional moments in the beam width direction is also presented.

Damage sensing in multi-functional hybrid natural fiber composites under shear loading

A comprehensive experimental study is performed to investigate the electro-mechanical response of jute/epoxy composites for in situ damage detection under in-plane shear loading conditions. By embedding carbon nanotubes (CNTs) in epoxy matrix and also reinforcing carbon fibers (CFs) using electro-flocking process between the jute laminates, a three-dimensional sensory network is generated inside the composites. A parametric study is conducted to examine the effect of two different weight percentages of CNTs (0.025% and 0.1%), two different CFs lengths (150 and 350 μm), four different CF flock densities (500, 1000, 1500, and 2000 fibers mm−2), and two different laminate orientations ((0-0-0-0)T and (0-90-0-90)T) on the generation of electrical conductive network and its role on damage detection. The electrical resistance values are measured using four circumferential ring probes measurement system. Results indicated that (0-0-0-0)T orientation showed 400% improvement in interlaminar shear strength compared to (0-90-0-90)T composites. CF flocking between the laminates experienced maximum increase of 50% in shear strength compared to non-flocked composites. For all composite types, there is no change in resistance during the elastic deformation of shear loading. Beyond elastic deformation, the increase in CF length and its density showed similar electrical response. The increase in CNTs concentration and laminate orientations did not show significant change in electrical response under shear loading conditions.

Strength of graphene grain boundaries under arbitrary in-plane tension

Understanding the tensile strength of graphene grain boundaries (GBs) is crucial for correlating the mechanical properties of two dimensional polycrystalline graphene with its atomic defect structure, a key to the success of large area graphene in many promising applications. Existing modeling studies mainly focus on the deformation and fracture of graphene GBs under tension that is perpendicular to the GBs. In reality, however, when a polycrystalline graphene is subject to a simple tension, random distribution of GBs in the graphene leads to arbitrary in-plane loading conditions of the GBs that cannot be fully understood with existing knowledge. To this end, we carry out systematic molecular dynamics (MD) simulations and also delineate a continuum mechanics model to investigate the failure strength of graphene GBs under tension in all possible loading directions. Particular focus is placed on quantitatively deciphering the interplay between GB misorientation angle and loading angle, and their effects on the failure strength of graphene GBs. Prediction from the continuum mechanics model based on a disclination dipole theory agrees well with the results from MD simulations. In this sense, the present study offers important insights on a better understanding of the mechanical properties of large area polycrystalline graphene.

An analytical investigation of the best stacking sequence of a symmetric laminated composite plate weakened by a hole

The investigation of the best set of fiber arrangements of a composite laminated structure under various loading conditions is very challenging and the analytical derivation is also complex when the laminate contains various shaped discontinuities. In this article, the best stacking sequence is investigated by treating it as an inverse problem, in which the best fiber arrangement is predicted considering maximization of the failure strength as an objective function. This inverse problem is solved using the hybrid genetic algorithm that operates the Tsai–Hill quadratic criterion as a fitness function and stacking sequence as design variables. A 4, 8 and 16-layered symmetrical laminated composite plate containing a triangular and square hole is optimized by considering the in-plane loading conditions, and the stresses in the Tsai–Hill quadratic criterion are calculated by an analytical solution of Muskhelishvili’s complex variable approach. The problem of the calculation of stresses and failure strengths from the estimated fiber arrangement data is presented as a forward problem. The effect of hole geometry and loading angle on an optimum design is also presented. The presented approach will be useful as an effective tool to study composites.

A comparative study of the extended forming limit diagrams considering strain path, through-thickness normal and shear stress

The substitute presentations of the conventional forming limit diagram (FLD) are stress-based forming limit diagram (FLSD), extended stress forming limit diagram (XSFLD), and polar effective plastic strain forming limit diagram (PEPS-FLD). These diagrams have already been proposed as alternative criteria to the conventional FLD for predicting forming limits in processes that sheet does not experience proportional or in-plane loading conditions. The present study provides a complete comparison of different forms of forming limit diagrams. For this purpose, FLD and extended FLDs are predicted based on the modified Marciniak and Kuczynski (M-K) model with Yld2011 anisotropic yield function while various factors that cause a change in the FLD of a specific alloy including initial imperfection coefficient (f0), non-linear strain path, through-thickness normal and shear stresses are considered. The results indicate that all forms of extended diagrams are independent of strain path and the diagrams in stress space (i.e., FLSD and XSFLD) are less sensitive to the strain path than PEPS-FLD. In this regard, the main weakness of XSFLD, especially on the right-hand side, is that the safety margin cannot be visualized easily. By increasing the initial imperfection coefficient, the level of all forms of diagram increases. However, the effect of through thickness stresses on different diagrams is not the same. Increase in normal and shear stresses results in a downward shift in FLSD and an upward shift in other types of forming limit diagrams.

Vibration and Buckling Analysis of Internally Cracked Square Plates by the MLS-Ritz Approach

Based on the classical thin plate theory, this paper proposes new sets of enriched basis functions for in-plane and out-of-plane displacements of square plates that can yield admissible functions for the Ritz method using the moving least-squares (MLS) approach. These admissible functions display the discontinuities of displacement and slope across a crack; give the correct singularity order for the stress resultants at the crack tips; and enhance the Ritz method’s ability to recognize the existence of an internal crack in a plate. To confirm the validity of the proposed approach, convergence studies were performed on the buckling loads and vibration frequencies of plates with central horizontal cracks, and the results obtained agree closely with the published ones as well as those generated by the commercial finite element software. To demonstrate the importance of including all the in-plane stress resultant components in the analysis, the effects of different in-plane stress resultant components on the buckling loads and vibration frequencies of simply supported center-cracked square plates under uniaxial uniform loading were investigated. The present approach was further employed to study the effects of cracks’ lengths, orientations, and locations on the buckling loads and frequencies of cracked square plates under different boundary conditions and in-plane loading conditions.

Elastic analysis of rectilinear orthotropic composite circular plates subject to transversal and in-plane load conditions using Ritz method

An analytical procedure for the analysis of elastic behavior of rectilinear orthotropic composite circular plate subjected to orthogonal and in-plane loads is presented. This kind of plates is composed of fiber-reinforced layers featuring fibers, differently oriented, arranged along rectilinear trajectories; composite lay-ups commonly employed for spot junctions are considered. The constitutive equations for rectilinear orthotropic composite circular plates are derived in the frame of classical lamination theory. The displacement components are determined, according to a novel approach, applying Ritz method to the virtual displacements principle for the load conditions treated in this work. The proposed framework is an approaching step for the theoretical definition of a Spot Joint Element able to simulate spot junctions (bolts, rivets or generic pins) applied to composite plates. To this purpose, displacement constraints deriving from the theoretical reference model of Spot Joint Element are considered. The employment of these specific boundary conditions required the derivation of suitable approximation functions, here reported in parametric form. Analytical results obtained by using the proposed procedure precisely match numerical results obtained by using refined FE models, for different aspect ratios of the plate and different laminate symmetrical lay-ups.

Cross laminated timber at in-plane beam loading – Prediction of shear stresses in crossing areas

Cross Laminated Timber (CLT) at in-plane beam loading conditions present a very complex stress state and many failure modes need to be considered in design. The work presented here aims at finding improvements of a specific analytical model for stress analysis and strength verification that has been suggested in literature and which is also suggested as a basis for design equations for the next version of Eurocode 5. Although the model has appealing properties it suffers from some drawbacks related to the assumed distributions of internal forces which, based on comparison to finite element analysis, appear to be inaccurate. The main focus in this paper is on model predictions regarding the distribution and magnitude of internal forces acting in the crossing areas between longitudinal and transversal laminations. The proposed modified model assumptions regarding the distribution of lamination shear forces, which in turn influence the forces acting in the crossing areas, are suggested to be taken into account in design of CLT beams.

Experimental study on seismic behavior of Un-Reinforced Masonry (URM) brick walls strengthened with shotcrete

In this study, the efficiency of conventional shotcrete technique for strengthening of Un-Reinforced Masonry (URM) walls was shown using an experimental program. In addition, in this program the possible benefit of using anchors for connecting the shotcrete reinforcement layer to the R/C foundation was studied. The experimental program consisted of testing five full scale specimens with two different height-to-length aspect ratios and so different failure modes, under in-plane cyclic loading conditions. Two specimens were tested as reference and others were strengthened on a single-face using shotcrete layer. According to the results, strengthening of URM walls using traditional shotcrete approach created a completely stiff panel and prevented the formation of cracks. The failure mode in both reference and strengthened short length walls was rocking and the shotcrete layer could increase the strength capacity, energy dissipation, and stiffness of wall due to yielding and rupture of steel bars anchored to the foundation. On the other hand, in strengthened long length walls, shotcrete layer increased the shear sliding capacity with no or small increasing in their rocking capacity. Therefore, the failure mode of strengthened walls converted from shear sliding to rocking, even in the specimen with anchorage system. The distributed type of anchorage system could not improve the strength capacity of long length wall. Anchorage system was able to improve the out-of-plane performance of strengthened walls.

Performance Analysis of Ply Orientation in Composite Laminates

With advancement in Material Sciences new types of materials are being invented and researched every day. Composite materials are globally used in aircraft design to decrease emissions and significant weight reduction. Advanced composite materials, which are usually continuous fibers (mostly carbon and glass) within a polymer matrix provide superior material properties than metals and enable lighter structural designs to be achieved in aerospace applications. In recent years, advanced composites have replaced traditional structural materials in aircrafts to a significant extent (e.g. Boeing 787, Airbus A350, with more than 50% composites by weight. The evaluation technique generally involves the implementation of ANSYS & MATLAB softwares that help in designing, drafting, and analysis. The scope of this paper is to highlight the researches done in composite laminates, new fibers and resins and to create future applications for composites. Eco-friendly resins will replace recycled plastics and bio-based polymers by composites. The present paper entitled “Performance Analysis of Ply Orientation in Composite Laminates” is the work done to perform the analysis on CFRP laminate with in-plane loading condition. In this research the mathematical calculation of determining the failure criteria of the laminate with ply orientation of [90/0/0/-45/+45]s is done by writing stress program on MATLAB and further analysis is performed using ANSYS. After obtaining both the results the design is validated.

Parametric studies on elastoplastic buckling of rectangular FGM thin plates

Considering Functionally Graded Material (FGM) plates composed of elastoplastic Ramberg–Osgood metal and elastic ceramic parts, the buckling phenomenon is studied. Plastic flows are formulated by the methods of Incremental Theory (IT) and Deformation Theory (DT). Using proper homogenization tactics and minimum potential energy principle, inclusive forms of governing equations are derived for the elastoplastic buckling of FGM plates. Using the Generalized Differential Quadrature (GDQ) technique a suitable solution algorithm is schemed and programmed in Matlab. Comparing the results with similar studies in buckling of elastoplastic homogeneous plates or elastic FGM plates, the methodology is assessed. The developed analytical IT and DT methodologies are used to analyze the elastoplastic buckling of plates with different boundary conditions. In different in-plane longitudinal and transversal loading conditions, the buckling load of plates with different thickness and aspect ratio are obtained. The effect of other several important factors such as the exponent of power law distribution function and the type of boundary conditions are studied in an extensive range of loads. Between similar FGM rectangular plates, the effect of aspect ratio and thicknesses upon the buckling loads are studied.