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1、精品论文A new method for fracture based on surface roughness in foil micro-deep drawing5YU Hailiang1,2(1. School of Mechanical, Materials, Mechtronic Engieering, University of Wollongong;2. School of Mechniacl Engineering, Shenyang University)Abstract: With the development of the micro-electro-mechanica
2、l systems (MEMS) technology and miniaturization of products, more attentions have been paid to the micro forming technology. The10paper proposed a new model which couples the Gurson-Tvergaard-Needleman damage model andrandom foil surface roughness distribution to investigate the fracture behavior of
3、 foils during micro-deep drawing. Results show that local non-uniform strain distribution due to the foil roughnessresults in crack occurrence. The calculated shape of fractured blank is in good agreement with experimental result. This study provides a new method to study the damage behavior in micr
4、oforming15process, and the findings are of guiding significance for understanding the damage behavior in the microforming process.Key words: Micro-deep drawing; ductile fracture; finite element method; stainless steel foil; surface roughness200IntroductionWith the development of the micro-electro-me
5、chanical systems (MEMS) technology and miniaturization of products 1, more attentions have been paid to the micro forming technology to improve through put for product development and creation along with the expansion of the market 2.25Surface roughness is an important factors that influence the qua
6、lity of a component, which has an impact on their functional performance 3, 4. In the micro-deep drawing process with decreasing the blank thickness, the surface roughness becomes the most important for the feasibility of micro forming processes, due to the increase of the surface to volume ratio wh
7、en scaling down process dimensions 5. Chang et al 6 found that smaller workpiece surface30roughness resulted in a low and constant friction in the early stage of the micro extrusion.An experimental program has been carried out for hydroforming of stainless steel micro-tubes by Zhuang et al 7. It was
8、 found that failure took place randomly, which was significantly different from observations of failure in hydroforming of macro-tubes by traditional macro Finite Element Method (FEM), where failure loads and locations were predictable. This35occurs because wall thinning of micro-tubes in forming pr
9、ocesses is non-uniform, i.e. localized necking takes place randomly. Damage mechanisms have to be understood for large plastic strain and complex multiaxial loadings 8. Wielage et al 9 found the fracture occurred at punch force levels well below those predicted by common equations. They pointed out
10、these phenomena couldbe accounted for by non-uniformity in the flow behavior of the material.40The FEM has been used in the simulation of the deep drawing process 10-15. Hu 10 used the size dependent FEM with friction functions to determine an optimum blank shape for a flange free rectangular micro
11、workpiece which was validated in experimental investigation. Manabi 11 et al used the two-dimensional finite element method to predict the roughness of workpiece during micro-deep drawing, but they did not consider the fracture behavior of materials. Ling et al 13, 1445used the Gurson-Tvergaard- Nee
12、dleman (GTN) ductile amage model to analyze the fractureFoundations: The financial support from the Vice-Chancellors Fellowship Grant at the University of Wollongong; the National Natural Science Foundation of China (51105071); Doctorate Foundation of the Ministry of Education of China (200900421200
13、05).Brief author introduction:University of Wollongong; Shenyang University. E-mail: - 6 -behavior of stainless steel sheet deep drawing, however, the surface roughness was not considered in models. In this paper, we firstly presented a three-dimensional finite element model considering both the dam
14、age and surface roughness of blank to study the fracture behavior during micro-deep drawing. The simulated shape of fractured blank is in good agreement with the experimental50result.1ModelFig. 1 shows the illustration of deep drawing process. The main geometrical dimension sizes are listed in Table
15、 1 11. The blank material is stainless steel (SUS 304) ultrathin foil of 23 m thickness.55Fig. 1 Illustration of deep drawing and dimension sizeTable 1. Geometrical parameters in deep drawing in Fig. 1 11ParametersValueDiameter of blank (DB), mm1.1Thickness of blank (TB), m23Diameter of drawing die
16、(DD), mm0.69Radius at corner of die (RD), mm0.1Diameter of punch (DP), mm0.654Radius at corner of punch (RP), mm0.1In the simulation, the punch, die and blank hold are considered as rigid. The GTN model is employed to simulate the fracture behavior of blank. GTN model, as shown in Eq. (1) 12, has60b
17、een proved successful to predict mechanical degradation and failure in tensile-dominantprocesses,(f )s eq f = () 2 + 2q fcosh 3 q 2s H ) - (1 + q 21 v3 Vs 02 s 0(1)where, f , fv is the void volume fraction. The parameters q1, q2, q3 are materials coefficients. For the SUS 304 stainless steel, the Yo
18、ungs modulus is 199 MPa, Poissons ratio 0.285, yield65stress 286 MPa, ultimate stress 668 MPa , and the true stress versus true plastic strain is listed inTable 2, other parameters in GTN model are listed in Table 3 13, 14.Table 2. Parameters of true stress versus true plastic strain adopted in FE m
19、odel 14True strain0.000.040.100.170.200.270.400.53True stress, MPa218385491604655761954112570Table 3. Main parameters in GTN model 13Parametersf0fcfFfN NSNq1q2q3Value0.0010.02230.1520.0040.30.11.51.02.25In the models, we assumed the maximum surface roughness peak is 500 nm. In the FE model, every el
20、ement was given a random roughness value from 0 to 500 nm.The three-dimensional geometrical model of the stainless steel foil micro deep drawing was established with the parameters above and meshed with quadrilateral elements by shell-type75elements. The roughness of the blank was considered in the
21、LS-DYNA model. Fig. 2 (a) shows the roughness distribution in a local zone in FE model. The whole FE meshing of deep drawing consider blank roughness is shown in Fig. 2(b). In the models, there are 107455 elements and108642 nodes, where 67043 elements and 67457 nodes for the blank. In deep drawing p
22、rocess, the punch presses at a constant speed. The Coulomb friction model is employed with the friction80coefficient set at 0.1.(a) Foil surface roughness(b) FE meshingFig.2 FE meshing of deep drawing process2Results85Fig. 3 (b) (h) shows the strain distribution around the crack initiation position
23、at different steps at the AA-BB zone of blank shown in Fig. 3 (a). Fig. 3 (b) and Fig. 3 (d) show the strain distribution at the AA-BB zone by the models without and with consideration of surface roughness at step 32, where the local strain non-uniform distribution is not obvious without considerati
24、on of surface roughness. Fig. 3 (c) (h) shows the strain distribution at AA-BB zone90with consideration of surface roughness. When the punch contacts with the blank, due to the surface roughness, the strain distribution is not uniform, as shown in Fig. 3(c). As higher the punch displacement, the str
25、ain in the blank increases. When the maximum strain reach 1.11, the defects first appear in a local zone owing to the non-uniform deformation 7, 9, as shown in Fig.3(g). When the defects appear, they propagates sharply.95Fig. 4 shows the crack propagation after crack initiation. First, the crack app
26、ears at the bending zone, and then, it propagates along the bottom corner, as shown in Fig. 4 (b). When the100105crack propagates about half way, the crack propagates to the flange, as shown in Fig. 4 (c) and (d). With increasing the punch displacement, the crack propagation speed decreases. Fig.5 s
27、hows the experimental fractured blank in Ref 15. The fractured shape of blank in Fig.4 (f) and Fig. 5 are in good agreement.Fig.3 Strain distribution around (a) fracture occurrence position for (b) without consideration of roughness at step 32 and with consideration of surface roughness at step (c)
28、1, (d) 32, (e) 36, (f) 40, (g) 44 and (h) 45Fig.4 Fracture evolution in micro deep drawing process at different steps(a) 44th step; (b) 45th step; (c) 46th step; (d) 47th step; (e) 48th step and (f) 48th stepFig. 5 Fracture in stainless steel blank during deep drawing 15110115Fig. 6 shows the roughn
29、ess change around the crack initiation zone during micro-deep drawing. Before the step 30, the roughness changes slightly. However, with further increasing the deformation step, the roughness increases gradually. When the crack initiation, the roughness around the zone increase greatly.Fig. 6 Roughn
30、ess around the crack initiation zone3ConclusionWith the GTN ductile fracture model and based on the surface roughness, the fracture of stainless steel foil during deep micro drawing was simulated by three-dimensional finite element method. Owing to the non-uniform strain distribution in local zone i
31、n blank, the crack occurs and propagates. Around the crack initiation zone, the roughness increases. The simulated result is in120125130135140145150155160165good agreement with the experiment.References1 Y.H. Seo, C.J. Park, B.H. Kim, H.J. Lee, N.K. Lee, Development of audio frequency vibration micr
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40、Finite element analysis of the formability of an austenite stainless steel sheet in warm deep drawing, J. Mater. Process. Technol. 143-144(2003) 242-248.一种基于表面粗糙度的分析微成型过 程断裂的方法喻海良1,2（1. 卧龙岗大学，机械、材料、机电学院，卧龙岗市，澳大利亚；2. 沈阳大学，机械工程学院，沈阳）摘要：随着微机电系统（MEMS）技术和小型化的产品的发展，越来越多的研究人员开始关注微 成 形 技 术 ， 以 适 应 市 场 扩 大 的 需要 。 本 文 提 出 了 一 种新 的 模 型 ， 偶 合 了Gurson-Tvergaard-Needleman 损伤模型和随机金属箔材表面粗糙度分布模型，用于研究微深 冲中金属箔材的断裂行为。结果表明，由于考虑了箔材的粗糙度，局部的非均匀应变分布导 致裂纹产生。计算出来的断裂形貌与实验结果吻合得很好。本研究为研究微成型过程中损 伤行为提供了一种新的方法，研究结果对人们认识微成型过程中的损伤行为具有指导意义。 关键词：微成型；韧性断裂；有限元；不锈钢箔片；表面粗糙度中图分类号：TG38