•Numerical model is developed to predict contact behavior in the fuel cell.•Numerical results show good agreements with experimental results.•Size effect resulting channel variation on contact behavior is proposed.•For η → 1, significant increase occurs in contact resistance and porosity.•Different assembly processes are needed when channel size is altered.Contact behavior between the gas diffusion layer (GDL) and bipolar plate (BPP) is of significant importance for proton exchange membrane fuel cells. Most current studies on contact behavior utilize experiments and finite element modelling and focus on fuel cells with graphite BPPs, which lead to high costs and huge computational requirements. The objective of this work is to build a more effective analytical method for contact behavior in fuel cells and investigate the size effect resulting from configuration alteration of channel and rib (channel/rib). Firstly, a mathematical description of channel/rib geometry is outlined in accordance with the fabrication of metallic BPP. Based on the interface deformation characteristic and Winkler surface model, contact pressure between BPP and GDL is then calculated to predict contact resistance and GDL porosity as evaluative parameters of contact behavior. Then, experiments on BPP fabrication and contact resistance measurement are conducted to validate the model. The measured results demonstrate an obvious dependence on channel/rib size. Feasibility of the model used in graphite fuel cells is also discussed. Finally, size factor is proposed for evaluating the rule of size effect. Significant increase occurs in contact resistance and porosity for higher size factor, in which channel/rib width decrease.

•Numerical model of sealing assembly is built to study sealing structure failure.•Two criteria are adopted to evaluate the risk of sealing structure failure.•Influences of material parameters and geometry parameters are discussed.•A guiding map of selecting proper parameters of sealing structure is proposed.Sealing stability in proton exchange membrane fuel cell (PEMFC) is critical to the performance and safety of stacks. However, sealing structure failure (SSF), which leads to the leakage of reactant gases, often occurs in the assembly process or start-up operation for PEMFCs. This study aims to investigate the effects of geometrical structure and material parameters of sealing components on the sealing structure failure. Slippage angle and slippage distance are adopted to evaluate the risk of SSF. Finite element (FE) simulations are conducted with consideration of the assembly process and start-up operation. Experiments are carried out to validate the accuracy of the FE model. Influences of parameters of gasket, membrane electrode assembly (MEA) frame, sealing groove shape of bipolar plate (BPP), and gas pressure are discussed in detail. Meanwhile, the risks of SSF for the stack by using metallic and graphite BPPs are compared. It is demonstrated that material properties and geometrical parameters of sealing components in PEMFC have great effects on SSF. The methodology developed is beneficial to the understanding of the SSF, and it can also be applied to guide the design of PEMFC stack assembly process to keep a good sealing reliability.

•Inherent strain theory is used to predict the transverse deformation of welded BPPs.•A novel angular distortion prediction model is proposed based on weld bead geometry.•A simplified method is proposed to determine the welding induced shape error of BPPs.•The shape error caused by welding distortion is up to 3.2 mm in two pass welded BPPs.Laser welding is the most effective joining method for thin metallic bipolar plates (BPPs) to achieve reliable seal and fulfill the requirements for fuel cell stacks. However, distortion caused by the welding heat will produce shape error in BPPs. The shape error will cause uneven assembly stress distribution and unacceptable contact resistance between BPPs and the gas diffusion layer (GDL), eventually affect the fuel cell performance.In this study, transverse deformation and angular distortion are considered to be the main sources of BPPs shape error and studied by modeling and experimental methods. An analytical model based on inherent strain theory is established to predict the transverse deformation of BPPs. Meanwhile, a model based on the weld pool geometry is proposed to evaluate the angular distortion. Experiments are performed to validate the models by welding 316L stainless steel sheets of 0.1 mm and 0.2 mm thick with a multi-mode fiber laser system. A good correlation is found between experimental results and the prediction models. Finally, a formula based on the former prediction models is proposed to calculate the welding induced shape error of BPPs with two pass welds. The formula is validated by experiments. The methodology in this study can be applied to guide the laser welding process design and manufacturing of the metallic BPPs.

•Contact pressure on the GDL is predicted using the continuous equivalent model.•Total contact resistance and porosity are proposed as evaluation indexes.•Numerical results show good agreements with experimental results.•Optimal clamping pressure is calculated as 0.67 MPa for the metallic BPP.Fuel cell assembly plays a dominant role in performance and lifetime of proton exchange membrane (PEM) fuel cell. Most current methods for assembly design are based on experiment and finite element (FE) model, which need high cost and huge computation for the whole fuel cell. Unfortunately, there are only few theoretical methods which contribute to the whole stack assembly, especially those in 3D model. This study develops a comprehensive methodology to simulate the stack assembly and to design the clamping displacement/pressure. At first, contact pressure field on the GDL is predicted with the use of the continuous equivalent model. The total contact resistance and porosity of fuel cell are proposed as the evaluation indexes combined by the desirability of function method. Then, in order to validate the contact pressure prediction, experiments with dimensional-error metallic bipolar plate are carried out and the numerical results show good agreements with experimental results. At last, clamping pressure of the endplate is calculated to optimize the assembly process. The methodology in this study is beneficial to the understanding of the internal contact behavior of the whole stack and helpful to guide the assembling of PEM fuel cell.

•The R2P imprinting method was proposed to create functional surface microstructures.•The size effects in the R2P micro/meso-imprinting process were investigated.•The increase of grain sizes leads to the decrease of rolling load significantly.•The formability of material could be enhanced with the increase of geometry sizes.•The surface deformation of materials is affected by the grain size and orientation.Roll-to-plate (R2P) imprinting process is an efficient technique to fabricate functional surface microstructures on a metallic substrate, which is widely used in the fields of microfluid, heat and mass transfer, and friction/drag reduction. However, the plastic deformation of microfeatures is significantly influenced by size effects. In this paper, the effects of grain and geometry size on the plastic deformation in R2P micro/meso-imprinting process were investigated by experiments and numerical simulations. According to the characteristics of the R2P micro/meso-imprinting process, a numerical model of R2P micro/meso-imprinting process was established. The experiments with pure copper were conducted through a self-developed R2P micro/meso-imprinting system. The size effects were studied via the evaluation of the formed height, rolling force and microhardness distribution. It is concluded that the rolling load reduces because of the decrease of flow stress caused by the weakening of grain boundary strengthening effect when the grain size increases. The wider groove and larger fillet could enhance the microforming ability of material and reduce the forming loads. The effect of groove width is more significant than that of the fillet. The microhardness distribution shows that the coarse-grained material has higher hardness than the fine-grained material in the central regions of the cross-section for the formed feature due to the penetration effect of deformation. However, the hardness in the central regions dwindles with the increase of the groove width and fillet. It is also found that the profile irregularity and surface roughness of the formed feature increase with the grain size and rolling depth. The results would provide a basis for further exploration in R2P micro/meso-imprinting process.

Physical experiments were conducted to study the effect of electric current on the shear strength of pressure-welded SS 316 sheet metals. Through experiments, it is found the shear strength first increases with the welding pressure, then decreases due to the excessive thinning. Higher current density leads to larger maximum shear strength. The numerical simulations of welding process were also carried out to explore the influence of current density on the bond formation: using the critical stress as the indicator of joining, the bond area is found to increase significantly with the current density from 5 Å/mm2 to 20 Å/mm2 when the thickness reduction is below 80%. The welding force required for successful joining also decreases with the increase of current density. Based on the simulations, the shear strength is further predicted by modeling the joining behavior and the results are corroborated and verified by experiments.

To combine the advantages of chromium nitride (CrN) and amorphous carbon (a-C) film, this study proposes a novel Cr–N–C multilayer film on 316L stainless steel (SS316L) as bipolar plates for proton exchange membrane fuel cells (PEMFCs) using closed field unbalanced magnetron sputter ion plating (CFUBMSIP) method. The characterizations of Cr–N–C film are analyzed by X-ray photoelectron spectroscopy (XPS), X-ray diffractometry (XRD), and scanning electron microscopy (SEM). Scratch tests indicate that the adhesion strength between the film and SS316L substrate has been greatly improved which is beneficial to prevent the multilayer film from spalling. Interfacial contact resistance (ICR) between coated SS316L sheets and simulated gas diffusion layer (GDL) decreases to 2.64 mΩ cm2 at 1.4 MPa. Potentiodynamic results reveal that the anodic corrosion potential of coated samples is more positive than the operation potential and the cathodic passivation current density is only 0.61 μA cm−2 at 0.6 V. Potentiostatic test, contamination analysis and surface morphology results reveal that the substrate is well protected by the Cr–N–C film. This research demonstrates that the novel Cr–N–C film exhibits excellent ex-situ performance including strong adhesion strength, high corrosion resistance and low ICR.Graphical abstractHighlights► A novel Cr–N–C multilayer film is deposited on SS316L as bipolar plates. ► Adhesion strength between the film and SS316L reaches 94.8 N. ► ICR is 2.64 mΩ cm−2 at 1.4 MPa and contact angle reaches 89.4°. ► Corrosion current density is 0.61 μA cm−2 at 0.6 V in cathodic environment.

•Fluctuation analysis is performed to explore the pressure distribution on GDL.•The effects of assembly force, BPP size and shape error are discussed respectively.•A response surface model is developed to predict the effect of shape error.•The maximum acceptable shape error is calculated as 1.52 mm for the metallic BPP.Thin metallic bipolar plate (BPP), due to mechanical strength, thermal conductivity, high power density, and relatively low cost, is considered to be an alternative to graphite BPP in proton exchange membrane (PEM) fuel cell. However, shape error of thin metallic BPPs is not avoidable due to its flexibility and springback in stamping process, as well as deformation resulted from thermal stress in welding process. In this study, fluctuation analysis is conducted and response surface methodology (RSM) is adopted to establish the relationship between shape error and contact pressure distribution on gas diffusion layer (GDL). Thin metallic BPPs made of stainless steel (SS) 304 sheets are fabricated and shape error is defined. Two types of specimens are selected and assembled with GDL. Effects of assembly force, BPP size and shape error are systematically investigated and a response surface model is developed to predict the effect on contact pressure distribution resulted from the shape error of BPP. The methodology in this study is beneficial to understand the effect of the shape error and predict the acceptable shape error. Based on the model, tolerance of the shape error of BPP is given to guide the manufacturing process of the thin metallic BPP.

In practice, the assembly error of the bipolar plate (BPP) in a PEM fuel cell stack is unavoidable based on the current assembly process. However its effect on the performance of the PEM fuel cell stack is not reported yet. In this study, a methodology based on FEA model, “least squares-support vector machine (LS-SVM)” simulation and statistical analysis is developed to investigate the effect of the assembly error of the BPP on the pressure distribution and stress failure of membrane electrode assembly (MEA). At first, a parameterized FEA model of a metallic BPP/MEA assembly is established. Then, the LS-SVM simulation process is conducted based on the FEA model, and datasets for the pressure distribution and Von Mises stress of MEA are obtained, respectively for each assembly error. At last, the effect of the assembly error is obtained by applying the statistical analysis to the LS-SVM results. A regression equation between the stress failure and the assembly error is also built, and the allowed maximum assembly error is calculated based on the equation. The methodology in this study is beneficial to understand the mechanism of the assembly error and can be applied to guide the assembly process for the PEM fuel cell stack.

A constitutive model has been developed to capture the rate-dependent large deformation behavior of the polypropylene (PP)/elastomer/inorganic filler ternary phase thermoplastic olefin (TPO). As the TPO exhibits elastic behavior of each constituent phase during elastic deformation and shear yielding of PP matrix after linear elastic loading. The elastic modulus of the composite is predicted using micromechanics theory. The viscoplastic behavior of TPO is described by a model which includes rate and temperature dependent yield, strain softening, and strain hardening. The material properties of the model are obtained from the uniaxial tensile test and then the model is examined for its ability to predict the response in deformation. It is proved that the large deformation features of the TPO composites are well described by the constitutive model.

Currently, a lot of know-how in conventional metal forming process cannot be directly applied to micro/meso forming processes due to so-called size effects. As a very important phenomenon in metal forming process, friction size effects are observed with an increasing degree of miniaturization. For microforming application, the input data of friction behaviors becomes critical to obtain accurate results for process simulation and traditional friction models are not reliable.In this paper, the evolution of friction behaviors from micro size to macro size is studied and a new uniform friction model is proposed based on the assumption of open-close lubricant pockets. A function of real contact area (RAC) αRCαRC and normal press p/σ0p/σ0 is established by introducing size/scale factor λλ to describe the influence of size effects. Therefore, the development of the friction behavior from micro/meso scale to macro scale could be depicted by this new uniform friction model. It indicates that the friction curves of micro/meso size are between those of the dry friction (upper boundary) and conventional lubricant friction (lower boundary). Moreover, finite element (FE) simulations are performed, based on the new friction model, to analyze the friction size effects in ring compression process. It is found that the radial friction forces with the change of inner and outer diameters are totally different and their tendencies are in good accordance with the experimental results. The new uniform friction model enables more flexible modeling of friction behaviors.

The deformation behavior of a thermoplastic olefin (TPO) during tensile loading has been studied by a finite element method (FEM). Dumbbell shaped specimens of the TPO were tested under various strain rates and temperatures. The test results were used to characterize the mechanical properties of this material. To capture the nonlinear rate-dependent response of the TPO, a physically based constitutive model [M.C. Boyce, D.M. Parks, A.S. Argon, 1988] for large strain deformation was used. The model includes rate and temperature dependent yield, strain softening, and strain hardening. The constitutive model was incorporated into a finite element code and was validated by comparison of predicted with measured results. A good correlation was found between the theoretical model results and the experimental data. Finite element analysis was also used to study neck propagation during tensile tests. Using the implemented constitutive model, necking was simulated and compared to experimental observations.

The stamped metal bipolar plate is a promising candidate of the traditional graphite plate for proton exchange membrane fuel cells (PEMFCs) due to its advantages, such as low cost, compactness, robustness and high production efficiency. This study proposes a new type of flow configuration, which is called slotted-interdigitated channel, for stamped metal bipolar plates. Numerical simulation of the flow distribution of slotted-interdigitated channels is studied by using three-dimensional computational fluid dynamics (CFD) and the results show the flow distribution is uneven. Consequently, an optimization model, based on a linear analytical model, is proposed to eliminate flow maldistribution. Finally, even flow distribution is obtained according to the optimum results and high fuel cell performance can be achieved.

Parallel channels have many advantages, such as low pressure drop and easy fabrication, but they may cause flow maldistribution which would result in low reaction efficiency. This study presents an analytical model to calculate the flow distribution of the parallel channels based on the assumption of the analogy between fluid flow and electrical network. The model, which ultimately releases from the solution of a set of nonlinear equations, is validated by comparing with the results obtained from three-dimensional computational fluid dynamics (CFD) simulations. Consequently, the model is used to optimize the geometric dimension of a parallel plate to obtain a uniform flow field distribution.

Different form traditional forming process, sheet soft punch process uses only a rigid die and the other tool set is a flexible medium, such as natural or synthetic rubbers. In this study, a kind of micro/meso sheet soft punch stamping process to fabricated micro channels is investigated via numerical simulations and experiments. Plane strain finite element analysis (FEA) models of different channel geometry (h/wh/w) are established to analyze the significant parameters associated with this process. Grain size of sheet metal and some key process parameters, such as the hardness of soft punch and lubricant condition, are detailed studied in this paper. Finally, the numerical results are partly validated by experiments.

Recently, the metallic bipolar plate (BPP) has received considerable attention because of its advantageous electrical and mechanical properties. In this study, a methodology based on FEA model and Monte Carlo simulation is developed to investigate the effect of dimensional error of the metallic BPP on the pressure distribution of gas diffusion layer (GDL). At first, a parameterized FEA model of metallic BPP/GDL assembly is established, and heights of the channel and rib are considered to be randomly varying parameters of normal distribution due to the dimensional error. Then, GDL pressure distributions with different dimensional errors are obtained respectively based on the Monte Carlo simulation, and the desirability function method is employed to evaluate them. At last, a regression equation between the GDL pressure distribution and the dimensional error is modeled. With the regression equation, the allowed maximum dimensional error for the metallic BPP is calculated. The methodology in this study can be applied to guide the design and manufacturing of the metallic BPP.

Resistance spot welding (RSW) is typically used in automobile body assembly, where continuous efficiency depends on electrode life, which is closely related with the water cooling effect. In this paper, the finite element simulation and response surface analysis methods are adopted to optimize the RSW electrode cooling process. Aiming to optimal cooling parameters and improve cool effect, we present a special sphere-shape weld cap with inlet pipe and cooling cavity and model its cooling effect as non-linear polynomial equations, which can avoid numerous influential factors. Electrode parameters, including pipe diameter, pipe height and flow velocity, are adjusted according to these non-linear equations. Optimization is carried out subsequently and experimental measurements on electrode diameters are performed for validation. It is found that the response surface model not only indicates the direction of design modification, but also leads to an optimal method for electrode design.

Bipolar plate is one of the most important and costliest components of polymer electrolyte membrane (PEM) fuel cells. Micro-hydroforming is a promising process to reduce the manufacturing cost of PEM fuel cell bipolar plates made of metal sheets. As for hydroformed bipolar plates, the main defect is the rupture because of the thinning of metal sheet during the forming process. The flow channel section decides whether high quality hydroformed bipolar plates can be successively achieved or not. Meanwhile, it is also the key factor that is related with the reaction efficiency of the fuel cell stacks. In order to obtain the optimum flow channel section design prior the experimental campaign, some key geometric dimensions (channel depth, channel width, rib width and transition radius) of flow channel section, which are related with both reaction efficiency and formability, are extracted and parameterized as the design variables. By design of experiments (DOE) methods and an adoptive simulated annealing (ASA) optimization method, an optimization model of flow channel section design for hydroformed metal bipolar plate is proposed. Optimization results show that the optimum dimension values for channel depth, channel width, rib width and transition radius are 0.5, 1.0, 1. 6 and 0.5 mm, respectively with the highest reaction efficiency (79%) and the acceptable formability (1.0). Consequently, their use would lead to improved fuel cell efficiency for low cost hydroformed metal bipolar plates.

Contact resistance between the bipolar plate (BPP) and the gas diffusion layer (GDL) plays a significant role on the power loss in a proton exchange membrane (PEM) fuel cell. There are two types of contact behavior at the interface of the BPP and GDL, which are the mechanical one and the electrical one. Furthermore, the electrical contact behavior is dependent on the mechanical one. Thus, prediction of the contact resistance is a coupled mechanical–electrical problem. The current FEM models for contact resistance estimation can only simulate the mechanical contact behavior and moreover they are based on the assumption that the contact surface is equipotential, which is not the case in a real BPP/GDL assembly due to the round corner and margin of the BPP.In this study, a mechanical–electrical FEM model was developed to predict the contact resistance between the BPP and GDL based on the experimental interfacial contact resistivity. At first, the interfacial contact resistivity was obtained by experimentally measuring the contact resistance between the GDL and a flat graphite plate of the same material and processing conditions as the BPP. Then, with the interfacial contact resistivity, the mechanical and electrical contact behaviors were defined and the potential distribution of the BPP/GDL assembly was analyzed using the mechanical–electrical FEM model. At last, the contact resistance was calculated according to the potential drop and the current of the contact surface. The numerical results were validated by comparing with those of the model reported previously. The influence of the round corner of the BPP on the contact resistance was also studied and it is found that there exists an optimal round corner that can minimize the contact resistance. This model is beneficial in understanding the mechanical and electrical contact behaviors between the BPP and GDL, and can be used to predict the contact resistance in a new BPP/GDL assembly.

Size effects make most know-how of traditional macro forming inappropriate for the micro forming process. Material behavior greatly varies in micro forming process with the decreasing of the scale. The purposes of this paper are to analyze the influence of material size effects and establish a martial model in micro/meso-scale. By combining surface model with theories of single crystal and polycrystal, a mixed material model, which contains a size dependent term and a size independent term, is proposed in this paper. It finds that the flow stress of material in micro/meso-scale is between that of single crystal model (lower bound) and polycrystal model (upper bound). Based on a mixed material model, the influence of size effects is discussed in both micro bulk forming process and micro sheet forming process. At the end, the validity of the mixed model is approved by comparing the simulations with the experimental results.

Multi-stand roll forming is a process that has very complicated deformation behaviour and shows significant nonlinearity. In this paper, the sensitivity analysis of parameters for multi-stand roll forming was performed via a new booting finite element method (FEM) model. Compared with the most of simulation, the new model is more consistent with production process and can account for the effects of roll rotating speed. Based on the model, the process of an open section channel formed with 10 passes was simulated and the sensitivity analysis was conducted with orthogonal experiment design combined FEM model. The multi-stand roll forming process can be efficiently analyzed by the new booting model. And sensitivity analysis shows the hardening exponent plays an important role in controlling the quality of the products.

To overcome the shortcomings of current technologies for meso-scale manufacturing such as MEMS and ultra precision machining, this paper focuses on the investigations on the meso milling process with a miniaturized machine tool. First, the related technologies for the process mechanism studies are investigated based on the analysis of the characteristics of the meso milling process. An overview of the key issues is presented and research approaches are also proposed. Then, a mesoscale milling machine tool system is developed. The subsystems and their specifications are described in detail. Finally, some tests are conducted to evaluate the performance of the system. These tests consist of precision measurement of the positioning subsystem, the test for machining precision evaluation, and the experiments for machining mechanical parts with complex features. Through test analysis, the meso milling process with a miniaturized machine tool is proved to be feasible and applicable for meso manufacturing.

The membrane electrode assembly (MEA) pressure distribution is an important factor that affects the performance of polymer membrane electrolyte fuel cell (PEMFC) stack. However, the general rules for assembly parameters that affect the MEA pressure distribution are hardly reported. In this study, a robust design analysis based on response surface methodology (RSM) was performed on a simplified fuel cell stack in order to identify the effect of assembly parameters on the MEA pressure distribution. The assembly pressure and bolt position were considered as randomly varying parameters with given probabilistic property and acted as the design variables. The max normal stress and normal stress uniformity of the MEA were determined in terms of the probabilistic design variables. The reliability of the robust design has been verified by comparing the robust solution with the optimal solution and an arbitrary solution.

In sheet metal assembly, not only the component variations and tool errors, but also the component structure (joint type) and assembly process (assembly sequence) affect the final dimensional quality. In this paper, a systematic method for adaptive joint design considering different assembly sequence is proposed to meet the in-process dimensional adjustability of KCs (key characteristics). First, the adaptive characteristic of the sheet metal joint is depicted. Then, the mathematical model in order for concurrently optimizing both joint type and different assembly sequence is presented. How to evaluate the combination of joint type and assembly sequence is carried out according to two conditions: (1) for single KC, and (2) for multiple KCs. The KC confliction is considered to ensure the important KCs. Genetic algorithm is used to resolve the optimization of joint design. An example is chosen to demonstrate our method finally, and various joint designs are acquired according to different assembly sequences by this means. The proposed methods make it possible for us to improve the dimensional quality of product in the design stage.

Part tolerance design is important in the manufacturing process of many complex products because it directly affects manufacturing cost and product quality. It is significant to develop a reasonable tolerance scheme considering the demands of cost and quality to reduce the production risk and provide a guide for supplier management. Traditionally, some kinds of cost objective functions or variation propagation models are often applied in part tolerance design. Moreover, designers usually solve the tolerance design problem by constructing a single-objective model, dealing with several single-objective problems, or establishing a comprehensive evaluating function combining several optimization objectives with different weights. These approaches may not adequately consider the interdependent and the interactional relations of various demands and balance them. This paper presents a kind of tolerance design approach at the early design stage of automotive parts based on the Shapley value method (SVM) of coalitional game theory considering the demands of manufacturing cost and product quality. First the part tolerance design problem is defined. The measuring data in regular production is collected instead of working on specific objective functions or design models. Then how the SVM is adopted to solve the tolerance design problem is discussed. Lastly, a tolerance design example of a vehicle front lamp demonstrates the application and the performance of the proposed method.

•A micro contact model is introduced to predict contact resistance between solid surface and porous material.•Carbon fiber paper is simulated by the random line network model based on the multi-layer construction.•Effect of large compression on contact behavior is taken into account.•Numerical results show good agreements with experimental results.•Based on the model, influences of carbon paper compression and main parameters are systematically discussed.Electrical contact resistance (ECR) at the interface is of significant importance in many fields of science and engineering. Current methods for contact resistance estimation are based on the typical nearly incompressible rough surfaces, which is not suitable for porous material with large deformation in the compression process. The objective of this work is to build an analytical model for ECR between solid material and porous material, for example, which could be used to predict power loss between carbon fiber paper and bipolar plate in the fuel cell. First, mathematical description of solid roughness surface is built by classic Greenwood and Williamson model. Considering the porous structure, carbon fiber paper is modeled by multi-layer construction based on random line network model. Effect of large compression of carbon paper on contact behavior is furtherly given necessary attention in this study. Contact pressure and resistance are calculated based on statistical methods with consideration of multi-deformation states. Then, experiments are carried out to validate the numerical model. The results show good agreements with the numerical model. Finally, influences of carbon paper compression and main parameters are systematically discussed based on the numerical model. The model developed will enhance our understanding regarding the relation between contact pressure and contact resistance at the interface for solid material and fiber-structure material.Download high-res image (399KB)Download full-size image

•The setups of forming limit testing were developed for meso scale sheet metals.•The forming limit curves (FLC) were developed for pure copper sheets.•The FLC shifts down with the decrease of thickness-to-grain-size ratio.•The GTN–Thomason coupled model was extended by considering the size effect.•The FLCs predicted based on the model agree with the experimental ones.Ductile fracture of metallic materials in micro/meso scale plastic deformation is influenced by geometry and grain sizes and the so-called size effect thus exists. To reveal how the size effect affects the formability of sheet metals in micro/meso scale plastic deformation, the forming limit of sheet metals was studied by experiment and modeling. An extended coupled damage model was first developed based on the Gurson–Tvergaard–Needleman and the Thomason models via considering the geometry and grain size effects on void evolution. In modeling process, the void nucleation was analyzed by taking account the phenomenon that the number of voids decreases with the ratio of thickness to grain size of workpiece. For the void growth, the widely used surface layer model was employed to describe the size effect on the flow stress of material. The grain size effect on void spatial arrangement was also modeled during the coalescence of micro voids. The model was then implemented into finite element simulations and the predicted forming limit curves under different scale factors were constructed. On the other hand, the forming limit experiments were conducted based on the miniaturized Holmberg and Marciniak tests to estimate the formability of sheet metals under different conditions. Both the physical experiments and finite element simulations show a significant size effect on the micro/meso scaled fracture behavior: The forming limit curve shifts down with the decreasing ratio of the thickness to grain size. The simulation results were also corroborated and verified by experiments. In addition, when the ratio is two or less than two, the very scattered limit strain results are observed in the experiments and the strain localization tends to occur at the beginning of deformation. The research conducted advances the understanding of size effect on the formability of micro/meso scaled sheet metals and thus helps the development of the successful and reliable microforming processes.

•A strain gradient elastic-viscoplastic model of amorphous polymers is proposed.•Size effects on both elasticity and plasticity of amorphous polymers are observed.•The elastic and plastic intrinsic lengths are 0.062 and 0.034 mm for PMMA.With the advantages of high-formability, low-cost and unique physical properties, polymers have been widely used in microforming of polymeric components for a large scale of applications in many fields including micro-optics, microfluidic and sensors, etc. In micro-scale, the deformation behaviors of polymers are observed to be size-dependent. Conventional constitutive models of polymers, however, cannot predict and represent those size-dependent behaviors well. To address this issue, a constitutive model with consideration of size effect for amorphous polymers in micro-scale was developed in this research. Firstly, on the basis of the couple stress theory, the impact of rotational gradients was taken into consideration and a strain gradient “elastic-viscoplastic” constitutive model was proposed to quantitatively describe the size-dependent behaviors of amorphous polymers in micro-scale. After that, four point micro-bending experiments were implemented on poly (methyl methacrylate) (PMMA) films with thickness varying from the millimeter scale to micrometer scale. The size effect of PMMA in micro-scale was further illustrated and the proposed strain gradient “elastic-viscoplastic” model was finally validated and verified for the capability of modeling of the size effect of amorphous polymers in micro-scaled deformation. This research thus advances the understanding of the size effect and the strain gradient based mechanical behaviors of amorphous polymers and facilitates its applications in industries.