Ultrasonic prediction ofR-value in deep drawing steels

The textures of five types of deep drawing steels were measured and analyzed using the series expansion method. Electromagnetic acoustic (EMAT) techniques were employed to determine the elastic anisotropy in terms of the angular variation of the ultrasonic velocities. The series expansion formalism was employed for predicting the elastic and plastic anisotropies from texture data. Comparison with the experimental measurements of Young's modulus indicates that the elastic energy method can accurately reproduce the elastic anisotropy if the single crystal elastic constants are appropriately chosen. The angular variation of ther-value in the rolling plane was calculated from the ODF coefficients by means of the pancake relaxed constraint model using an appropriate CRSS ratio for glide on the {112} 111 and {110} 111 slip systems. The fourth order and first sixth order ODF coefficients were calculatednondestructively from the anisotropy of the ultrasonic velocities. The calculated pole figures based on the ODF coefficients obtained in this way are similar to those derived from complete X-ray data. It is shown that the plastic properties of commercial deep drawing steels are predicted more accurately when the 4th-and 6th-order ODF coefficients are employed than when only the 4th-order ones are used.     

The influence of the drawing parameters and temperature rise on the prediction of chevron crack formation in wire drawing

The objective of the present work is to predict the formation of chevron crack in copper wire drawing process. The first part of this paper is to determine the chevron crack formation initiated by a central burst inside the wire material using experimental tests. These results are compared with results from a series of numerical simulations using the Cockcroft?CLatham fracture criterion. The second part of this work concerns the determination of a curve that divides the chevron and safe zones for a better wire drawing process. The conditions of central burst defects formation along the wire axis depend on drawing parameters and friction coefficient between the die and the wire. The friction coefficient is defined as a linear function of temperature rise which is measured close to the wire-die interface. The obtained results show that the friction coefficient depending on temperature rise during wire drawing has an impact on the damage of copper wire.     

Hot deep drawing of titanium sheet

Abstract

Commercial purity titanium (IMI 125) and a Ti–Cu alloy (IMI 230) in sheet form have been deep drawn at room temperature and at elevated temperatures. Cylindrical cups drawn at room temperature and at temperatures up to about 550°C develop four ear peaks at about 45° to the rolling direction (RD). When drawing is carried out at temperatures above 600°C, two ear peaks are formed at 90 and 270° to RD. The change in anisotropy is attributed to the temperature dependence of crystallographic slip modes, the high temperature behaviour being associated with basal plane slip. Drawing with a temperature gradient (cold punch, heated die) enables high drawing ratios to be achieved.

MST/1352     

Influence of tool geometry variations on the limiting drawing ratio in micro deep drawing

In this study, the impact of different tool geometries on the limiting drawing ratio (LDR) in micro deep drawing was investigated. Experimental micro deep drawing tests to determine the limiting drawing ratios were carried out for a variation of the punch diameter, the die radius and the die clearance. In order to assess the impact of the material properties on the process limits the foil materials Al99.5 and E-Cu58, both with a thickness of 20 μm, and the stainless austenitic nickel-chromium steel 1.4301 (X5CrNi18-10) with a thickness of 25 μm were investigated. The results reveal an increase of the limiting drawing ratio with increasing die radius size for the foil materials E-Cu58 and austenitic steel. For a decrease of the die clearance to values smaller than 1.25 times the foil thickness an increase of the limiting drawing ratio was determined for all three materials.     

Analysis of sheet steel fracture during deep drawing

Low-carbon steel sheet used for the fabrication of automotive brake components was tearing during deep drawing. The associated mill certificates revealed that the coil met the specified chemical composition and mechanical properties. Metallographic evaluation revealed a severe variation with respect to grain size through the thickness of the steel sheet, as well as a slight segregation of pearlite. Insufficient temperature during hot rolling in combination with a high coiling temperature resulted in the observed microstructural gradient. The anisotropic mechanical properties were amplified by the slight carbon segregation.     

简单形状零件拉深成形智能化控制技术研究

板材成形智能化是冲压工艺的一项新技术.以圆锥形件和锥壁盒形件为研究对象,分别讨论了实现实时监测、实时识别、实时预测和实时控制所需的关键技术,逐步形成了拉深成形智能化控制的理论基础.在实时识别和实时预测阶段采用人工神经网络,在压边力控制阶段采用基于破裂临界曲线的控制方法,能够得到较满意的结果.研究过程中开发了智能化拉深实验系统,实验证明识别、预测精度较好.     

Experimental validation of numerical sensitivities in a deep drawing simulation

Deep drawing of a benchmark B-pillar is numerically modelled and experimentally performed with varying blankholder force and several blank shape parameters. The most influential parameters are selected for optimisation. Direct application of Autoform sigma software was used to determine sensitivities, as well as indirect application using response surfaces. Interesting nonlinear sensitivities were found that will be missed with simple linear screening techniques.     

Numerical analysis of hydroforming deep drawing of conical cup

Aided by the FE-code, analysis is carried to find the proper hydroforming deep-drawing condition for the perfect forming of a conical cup that can not be drawn successfully by conventional deep drawing method. Hydraulic counter pressure must be reasonably controlled, otherwise defects such as fracture and wrinkling can not be avoided. Therefore, the forming procedure is divided into three stages, and the counter pressure is adjusted intentionally to make the blank clamped onto the punch at a suitable time, then deformation at dangerous area is resisted by the effect of the counter pressure and the conical cup can be formed without defects.     

Allocation of variance reduction targets under the influence of supplier interaction

A common quality improvement strategy used by manufacturers is to periodically allocate quality improvement targets among their suppliers. We propose a formal modelling and optimization approach for assessing quality improvement targets for suppliers. In this approach it is understood that a manufacturer's quality improvement results from reductions in supplier process variances, which occurs only through investments in learning. A constrained nonlinear optimization model is developed for determining an optimal allocation of variance reduction target that minimizes expected total cost, where the relationship between performance measures and the set of design parameters is generally represented by second-order polynomial functions. An example in the fabrication of a tyre tread compound is used both to demonstrate the implementation of our proposed models as well as to provide an empirical comparison of optimal learning rates for different functional relationships between the performance measures and the set of design parameters.     

The manufacture of ultra-high modulus polyethylenes by drawing through a conical die

Various grades of linear polyethylene have been drawn through a heated conical die at 100° C. It was found that after a suitable start-up procedure, continuous drawing was possible in all cases with a stable neck region extending beyond the die exit. The degree of deformation attainable was found to depend strongly on the draw velocity. Very high deformation ratios could be obtained and the Young's moduli of the die-drawn products were comparable to those of similar products obtained by solid state extrusion and tensile drawing, reaching values as high as 60 GPa. The effects of molecular weight and co-polymerization are substantial, but not exactly analogous to those previously observed in hydrostatic extrusion and tensile drawing. This is probably due to the non-isothermal nature of the final stage of deformation in the case of die drawing.     

Characterization of the material elongation in the deep drawing of paperboard

In this paper, deep‐drawn paperboard cups are characterized in terms of their elongation along the cup wall. For this purpose, a method for the non‐destructive determination of the elongation was developed and tested. Using the presented method, a parameter study of the process parameters blank holder force, forming temperature, material moisture content, drawing velocity, and clearance ratio was performed. The influence of the process parameters on the cup wall elongation was determined by statistical design of experiments. Using the determined relationships between the process parameters, it was possible to achieve a shape‐specific characterization of the elongation along the cup wall. The parameter study showed a significant influence of the blank holder force, the forming temperature, and the material moisture content to the elongation along the cup wall.     

Blank design optimization on deep drawing of square shells

A numerical scheme for improving the drawability in the deep drawing of square shells by blank design optimization is presented. The numerical scheme is formulated as an optimization problem whose objective is to maximize the drawability, subject to the constraint that fracture failure and draw-in failure do not occur. Appropriate blank design parameters are used as the design variables of the formulation. To enable the numerical scheme to work models predicting the onset of fracture failure and draw-in failure are required. Numerical models simulating the onset of these failures under the given process conditions are thus discussed. Optimal designs for three cases are then presented. Finally, by considering both the drawability and the non-uniformity of the final flange profile it is shown that the circular profile can be considered to be the optimal blank shape for square cup drawing.     

Numerical simulation and experimental validation of a multi-step deep drawing process

This paper presents the numerical simulation of an industrial multi-step deep drawing process. A large strain finite element formulation including a hyperelastic elastoplastic constitutive model and a contact-friction law is used to this end where the steel sheet material parameters considered in the analysis are previously derived through a characterization procedure of its mechanical response. The numerical predictions of the final shape and thickness distribution of the blank are compared and discussed with available experimental values measured at the end of three successive drawing steps. In addition, a plastic work-based damage index is used to assess failure occurrence during the process. The damage values computed at the end of the drawing process are found to be lower than that corresponding to rupture in the tensile test, considered here as the threshold of failure, confirming, as observed experimentally, that neither fracture nor necking is developed in the blank during the whole drawing process. Finally, the possibility to carry out a reduced two-step drawing process, obtained by merging the second and third steps of the three-step process, is precluded since the damage criterion predicts in this case excessively large values that indicate that failure may occur in specific zones of the sheet.     

Enhancement and prediction of modulus of elasticity of palm kernel shell concrete

This paper presents results of an investigation conducted to enhance and predict the modulus of elasticity (MOE) of palm kernel shell concrete (PKSC). Scanning electron microscopic (SEM) analysis on palm kernel shell (PKS) was conducted. Further, the effect of varying sand and PKS contents and mineral admixtures (silica fume and fly ash) on compressive strength and MOE was investigated. The variables include water-to-binder (w/b) and sand-to-cement (s/c) ratios. Nine concrete mixes were prepared, and tests on static and dynamic moduli of elasticity and compressive strength were conducted.     

Assessment of anisotropic hardening models for conventional deep drawing processes

Assessing the predictive capabilities of recent advanced constitutive modelling approaches for processes with industrial complexity is a challenging task. Real process conditions such as blankholder pressure distribution, friction and tool elasticity sensitively affect experimental observations, making the isolation of constitutive effects difficult. A systematic approach is proposed in this work to assess the performance of anisotropic hardening models with the least possible disturbance from process conditions. Two deep drawing examples were used for these purpose (“cross die” and “lackfrosch”) in conjunction with a mild steel (DC05). Optically measured strain distributions have been compared to corresponding simulations, which have been calibrated to accurately match the measured blank draw-in. The effect of initial yield locus shape as well as anisotropic hardening effects have been discussed.     

Forming sheet metals by means of multi-point deep drawing method

Multi-point deep drawing (MPDD) is an advanced manufacturing technology for 3D sheet metal parts and it can form a variety of part shapes without the need for solid dies. In this study, a test set has been prepared for multi-point deep drawing process utilizing the multi-point forming technology. Drawability attributes of gradually rectangular shaped container have been observed using a sheet, which has the quality of Erdemir 7114 and is suitable for deep drawing process, and also using multi-pointed punch with a given tool geometry and a draw velocity. The blank shape to be drawn without wrinkling and tearing has been determined. Wrinkles and dimples are the major forming defects in the MPDD process. In conventional deep drawing, the method to form sheet metal with a blank holder is an effective way to suppress wrinkling; and the same is true in MPDD. The process of multi-point forming technology decreases production cost of die, provides flexible usage, and it is convenient to achieve the most even deformation distribution.     

Tangent modulus tensor in plasticity under finite strain

Summary The tangent modulus tensor, denoted as , plays a central role in finite element simulation of nonlinear applications such as metalforming. Using Kronecker product notation, compact expressions for have been derived in Refs. [1]–[3] for hyperelastic materials with reference to the Lagrangian configuration. In the current investigation, the corresponding expression is derived for materials experiencing finite strain due to plastic flow, starting from yield and flow relations referred to the current configuration. Issues posed by the decomposition into elastic and plastic strains and by the objective stress flux are addressed. Associated and non-associated models are accommodated, as is plastic incompressibility. A constitutive inequality with uniqueness implications is formulated which extends the condition for stability in the small to finite strain. Modifications of are presented which accommodate kinematic hardening. As an illustration, is presented for finite torsion of a shaft, comprised of a steel described by a von Mises yield function with isotropic hardening.Notation B strain displacement matrix - C=F ^T F Green strain tensor - compliance matrix - D=(L+L ^T )/2 deformation rate tensor - D fourth order tangent modulus tensor - tangent modulus tensor (second order) - d VEC(D) - e VEC() - E Eulerian pseudostrain - F, F _e ,F _p Helmholtz free energy - F=x/X deformation gradient tensor - f consistent force vector - residual function - G strain displacement matrix - h history vector - h time interval - H function arising in tangent modulus tensor - I, I ₉ identity tensor - i VEC(I) - k ₀,k ₁ parameters of yield function - K _g geometric stiffness matrix - K _T tangent stiffness matrix - k _k kinematic hardening coefficient - J Jacobian matrix - L=v/x velocity gradient tensor - m unit normal vector to yield surface - M strain-displacement matrix - N shape function matrix - n unit normal vector to deformed surface - n ₀ unit normal vector to undeformed surface - n unit normal vector to potential surface - r, R, R ₀ radial coordinate - s VEC() - S deformed surface - S ₀ undeformed surface - t time - t, t ₀ traction - t VEC() - VEC( ) - t VEC() - t _r reference stress interior to the yield surface - t t–t _r - T kinematic hardening modulus matrix - u=x–X displacement vector - U permutation matrix - v=x/t particle velocity - V deformed volume - V ₀ undeformed volume - X position vector of a given particle in the undeformed configuration - x(X,t) position vector in the deformed configuration - z, Z axial coordinate - vector of nodal displacements - =(F ^T F–I)/2 Lagrangian strain tensor - history parameter scalar - , azimuthal coordinate - elastic bulk modulus - flow rule coefficient - twisting rate coefficient - elastic shear modulus - iterate - Second Piola-Kirchhoff stress - Cauchy stress - Truesdell stress flux - deviatoric Cauchy stress - Y, Y yield function - residual function - plastic potential - X, Xe, Xp second order tangent modulus tensors in current configuration - X, Xe, Xp second order tangent modulus tensors in undeformed configuration - (.) variational operator - VEC(.) vectorization operator - TEN(.) Kronecker operator - tr(.) trace - Kronecker product     

A study of the variations in elastic modulus and its effect on springback prediction

A model is proposed in order to evaluate the variation of the elastic modulus of metallic materials due to both damage and dislocations rearrangements leading to non-linear recovery. It is an elastic plastic model with varied unloading elastic modulus and coupled with damage. This model allows obtaining more accurate prediction of material behavior, starting from a virgin state and finishing by failure. Simulations have been carried out in uniaxial tensile test and the predicted results show good agreement with experiments. The L-bending test is also simulated and the proposed model allows obtaining more accurate springback prediction.