1、附錄 A 外文文獻Effects of geometry and fillet radius on die stresses in stamping processesAbstract: This paper describes the use of the finite element method to analyze the failure of Keywords: Stamping; Metal forming; Finite element method; Die failure 1. IntroductionIn metal forming processes, die failu

2、re analysis is one ofthe most important problems. Before the beginning of thisdecade, most research focused on the development of the-oretical and numerical methods. Upper bound techniques1,2 , contact-impact procedures 3 and the finite elementmethod (FEM) 4,5 are the main techniques for analyzingst

3、amping problems.6-12With the development of computertechnology, the FEM becomes the dominant technique . Altan and co-workers 13,14 discussed the causes offailure in forging tooling andpresented a fatigue analysisconcept that can be applied during process and tool design toanalyze the stresses in to

4、ols. In these two papers, they usedthe punching load as the boundary force to analyze the stressstates that exist in the inserts during the forming process anddetermined the causes of the failures. Based on these concepts, they also gave some suggestions to improve diedesign.In this paper, linear st

5、ress analysis of a three-dimensional(3D) die model is presented. The stress patterns are thenanalyzed to explain the causes of the crack initiation. Somesuggestions about optimization of the die to reduce the stressconcentration are presented. In order to optimize the designof the die, the effects o

6、f geometry and fillet radius arediscussed based on a simplified axisymmetric model.2. Problem definitionThis study focuses on the linear elastic stress analysis ofthe die in a typical metal forming situation (Fig. 1). The die(Fig. 2) with a half-moon shaped ingot on the top surface ispunched down to

7、wards the workpiece which is held insidethe collar, and the pattern is made onto the workpiece.Cracks were found in the die after repeated operation: (i)when the die punched the workpiece, there is crack initiationbetween the tip of the moon shaped pattern and one of theedges (Crack I); and (ii) aft

8、er repeated punching, there isalso a crack at the fillet of the die (Crack II).The present work was carried out with the followingobjectives: (i) to establish the causes of the crack initiation;and (ii) to study the effects of geometry and fillet radius.3. Simulation and analysis3.1. 3D simulationTh

9、e simulation is performed with the FEM code Abaqus 15 . Twomeshes are created for- 1 -：蓋板零件的沖壓工藝及模具設(shè)計the die shown in Fig. 3a andb. The 3D solid elements for the workpiece are C3D8 (8-node linear brick) elements. There are about 4000 nodes and3343 elements in the coarse mesh model, and 7586 nodesand

10、 6487 elements in the fine mesh model. The boundarycondition involves fixing the bottomof the die, i.e., U 2=0 forall the nodes on the die bottom. A pressure of 200 MPa isapplied on the top surface of the half-moon pattern. Youngsmodulus is 200 GPa and Poissons ratio is 0.3.In order to analyze the p

11、rincipal stress concentration areain the region of Crack I, different cases are studied. Let themodels shown in Fig. 3a and b be Case 1. A new 3D model(Case 2) is used as shown in Fig. 3c. The die is separated intothree parts. The Abaqus command *CONTACT PAIR, TIEDis used to tie separate surfaces to

12、gether for joining dissimilarmeshes. The advantage of this model is its convenience inchanging the mesh of the half-moon pattern and its position.First, the half-moon pattern is moved 6 mm towards thecenter (Case 3) as shown in Fig. 3d. Second, the fillet radiusof the half-moon pattern is changed fr

13、om 0 to 0.5 mm (Case4) as shown in Fig. 3e.3.2. Results and discussionFor the two meshes used in Case 1. The maximumprincipal shear stress (S12) distribution at the region of fillet are shown in Fig. 4a and b. The results show thatthe stress distribution patterns are the same for the twodifferent me

14、shes, and therefore, the convergence of thesolutions is established.Altan and co-workers 14 have presented the stressanalysis of an axisymmetric upper die. In their work, whenthe material of the workpiece flows to fill the volumebetween the dies and collar, the contact surface of the dieis stretched

15、. At the area of the transition radius, the principalstresses change direction and reach high tensile values.According to their analysis, the fatigue failure is due totwo factors: (i) when the stress exceeds the yield strength ofthe die material, a localized plastic zone generally formsduring the fi

16、rst load cycle and undergoes plastic cyclingduring subsequent unloading and reloading, thus microscopic cracks initiate; and (ii) tensile principal stresses causethe microscopic cracks- 2 -to grow and lead to the subsequentpropagation of the cracks.The VonMises stress distribution is shown in Fig. 5

17、a. Veryhigh stress occur in the half-moon and fillet regions. If thecontact pressure keeps increasing, plastic zones will form first in these two regions.Fig. 5b shows the maximum principal stress (SP3) distribution pattern. In order to show the area of Crack Iinitiation, Fig. 5c provides a zoomed v

18、iew of the area. Itis clear that a tensile principal stress (SP3) concentration of25.5 MPa exists between the half-moon pattern and the freeedge and is the cause of crack initiation.Since Crack I propagates nearly normal to the 1-2 plane,the direction of the stresses which cause the crack initiation

19、must be parallel to that plane. Fig. 5d shows the direction ofthe maximum principal tensile stress at node 145 andconfirms Crack I is normal to the 1-2 plane.After repeated punching, Crack II initiates in the filletregion, and gives rise to fatigue failure. The geometry in thelocal area is very simi

20、lar to the case which Altan and co-workershave analyzed. However, there are no contactstresses in that area for the present case, and Fig. 5b showsthat the maximum principal stresses are all compressive atthe fillet. Fig. 5e shows that there is high shear stress (S12)concentration at the fillet whic

21、h is about 30 MPa. The shearstressesseem to be the stresseswhich lead to the initiationand propagation of cracks.The results of the four cases (Cases 1-4) for the largestmaximum principal stresses are listed in Table 1.When the number of elements for the half-moon pattern isincreased from 10 to 70,

22、the largest principal stress at theposition of Crack I initiation is increased by(30.5-25.5)/30.5=16%(Case 2). The principal stresses are very sensitiveto the half-moon pattern.Cases 2-4 show the effect of location of the half-moonand its fillet radius. If the half-moon pattern is moved 6 mmtowards

23、the center, the largest principal stress at the positionof Crack I is reduced by (25.3-30.5)/30.5=-17% (Case 3).If the fillet radius of the half-moon pattern is changed to0.5 mm, the principal stress is reduced (28.5-30.5)/30.5=-7% (Case 4). Therefore both these methods can reduce the stress concent

24、ration, the first being more effective.- 3 -：蓋板零件的沖壓工藝及模具設(shè)計Effects of geometry and fillet radius on die stressdistribution2D modelingIn order to optimize the die, the effects of geometry and fillet radius on die stress distribution are discussed further.An axisymmetric model is used (Fig. 6) for the

25、 analysis.Initially, the radius r1 of the inner cylinder is set to 10 mm,the height h of the inner cylinder is set to 5 mm, and theheight H of the outer cylinder is set to 25 mm. Also, r2 istheradius of the outer cylinder, and the ratio r2/r1 is changedfrom 1.2 to 1.5, 2.0, 3.0 and 4.0. The radius R

26、 of the fillet ischanged from 2.0 to 0.5 mm, and h is changed from 5 to 2and 0The pressure is given as 200 MPa at the topsurface. The nodes at the bottom edge are fixed, and allothers are free to translate (exceptthose on the axis in theradial direction).4.2. Results and discussionA total of 30 case

27、s were studied. Parameters that arevaried include2 /r1 ratio, h,and fillet radius R. These 30cases are shown in Table 2. For all cases,1isr fixed at 10 mmand H is fixed at 25 mm.2/r1The effect of varying the r 2/r1 ratio is examined for caseswith the value of h fixed at 5mm.Fig. 7a-c with the value

28、of h fixed at 5 mm and varyingratio of r2/r1 shows that the maximum value of the principalstress (SP3) reduces with increasing 2r/r1, and changes inposition from a point on the surface to below the surface.This trend is reflected in Fig. 8a.On the other hand, Fig. 8b indicates that the maximumshear

29、stress (S12) becomes larger with increasing ratioof r2/r1. The rate of this increase drops with increasingr2/r1. The shear stress patterns for some cases are shown inFig. 7f-h.The effect of height h of the inner portion is examined forthree cases with h=0, 2 and 5 mm with R fixed at 2 mm.From Fig. 8

30、a, it can be seen that the maximum principalstress (SP3) increases marginally with increasing h up tor2/r1 of 2, afterwhich the trend is reversed. However, forlarge h, the effect becomes less important. On the otherhand, the maximum shear- 4 -stress is higher with increasing hfor the same r 2/r1 rat

31、io. Stress patterns are shown in Fig.7a,d-f, i and j.The effect of fillet radius R is examined for two cases withR=0.5 and 2 mm. The results are shown in Fig. 8c and d. Itcan be seen that for r 2/r1 larger than 2, the maximumprincipal stress (SP3) is relatively insensitive to changesin the fillet ra

32、dius. For r2/r1 ratio less than 2, a larger filletradius results in a larger principal stress. However, thechanges in the principal stress are less drastic comparedwith the changes in the maximum shear stress (S12) shownin Fig. 8d.From Fig. 8d, it can be seen that themaximum shear stressnearly doubl

33、es when the fillet radius is reduced from 2 to0.5 mm for the same 2r/r1 ratio. Stress patterns are shown inFig. 7a, f, k and l.Fig. 8. Showing: (a) SP3 forr /rr /r2 1=1.2-4.0, h=0-5 mm, R=2 mm; (b) S12 for2 1=1.2-4.0,h=0-5 mm, R=2mm; (c) SP3 for r/r =1.2-4.0, h=5 mmR=0.5 and 2 mm; (d) S12 forr /r=1.

34、2-4.0, h=5 mm, R=0.5 and 22121mm.Based on the above analysis, some possible optimumsolutions for the axisymmetric model can be achieved, asbelow.Both the maximum principal stress (SP3) and maximumshear stress (S12) are larger with increasing h. Thus, hshould be relatively small.With changes in R, th

35、e values of SP3 and S12 showdifferent trends. If the maximumprincipal stress is morelikely the cause of die failure, R should be changed to asmaller value. Conversely,if the maximum shear stressis the cause, R should be larger. Generally speaking,- 5 -：蓋板零件的沖壓工藝及模具設(shè)計thevalue of R should be between 1

36、.5 and 2.0 for thedimensions used here.The effects of r 2/r1 on SP3 and S12 are significant whenr 2/r1 is less than 2. However, the trends are different. Ifthe maximum principal stress is the cause of die failure, r2/r1 should be changed to a larger value, otherwise2/r1should be smaller.5. Conclusio

37、nsThe finite element code Abaqus has been used for diestress analysis. A 3D model is used to analyze the differentmechanisms of crack initiation. This method not only pre-dicts the causes of cracks, but also the direction of crackpropagation.Subsequently, a 2D model is used to study the effects ofdi

38、e geometry and fillet radius on the stress distribution.Some guidelines on die design are given. At the early stageof die design, the FEM can help to predict possible failureand to optimize die design so as to save cost and time. Theresults are valuable both in theoretical research and indus-trial a

39、pplication.- 6 -沖壓工藝中幾何及內(nèi)圓角對模具應力產(chǎn)生的影響摘要： 本文描述使用有限元法分析沖壓工藝中產(chǎn)生的模具故障問題。在以下問題中，模具的不同位置出現(xiàn)裂紋，這些可以歸為機械裝置領(lǐng)域。裂紋出現(xiàn)的原因之一在于主應力，原因之二在于剪應力。 本文使用 3D 模型來模擬這些問題。 3D 模擬圖使本文分析的問題簡化成軸型問題。關(guān)鍵詞： 沖壓 金屬成型有限元法模具故障簡介金屬成型過程中， 分析模具故障是重要問題之一。 21 世紀初，大多數(shù)研究專注于理論和數(shù)字化方法。上限分析，沖擊接觸程序以及有限元法，是分析沖壓工藝的三種主要方法。隨著電腦科技的發(fā)展，有限元法成為突出的分析技術(shù)。埃爾頓及其合

40、作者討論了鍛造工具失敗的原因， 并且展示了可應用于工序和工具設(shè)計的疲勞分析理念。在其兩頁的文章中，他們使用沖剪載荷作為邊界力來分析成型過程中所受的應力情況，并且確定故障出現(xiàn)的原因。在此理念下，他們也給模具設(shè)計提出了建議。在這篇文章里，用線性應力分析3D 模擬圖，因此，應力圖用來解釋裂紋產(chǎn)生的原因。本文也提出了一些減少應力集中以優(yōu)化模具的建議。為了優(yōu)化模具設(shè)計， “幾何及內(nèi)圓角對模具的影響”放在簡化的軸形圖上討論。2 問題說明本項研究專注于典型金屬成型過程中模具的線彈性應力分析。如圖 1 所示。圖 2 中，上表面的半月形模塊向下朝軸環(huán)內(nèi)的工件運動，模塊嵌入工件內(nèi)。反復操作后，模具上出現(xiàn)裂紋 1，

41、當模具碰撞工件時， 在半月形模塊和一個邊緣之間出現(xiàn)裂紋1；(2) 反復碰撞后，模具圓角上出現(xiàn)裂紋2。本篇文章的研究目標：（ 1）確定裂紋產(chǎn)生的原因， （2）研究幾何及內(nèi)圓角的作用。圖 1. 典型金屬成型過程圖2.沖模裂紋1 和 2模擬和分析3.1 3D 模擬模擬圖使用有限元。 如圖 3 中 a 和 b 所示的兩個網(wǎng)格圖。三維實體單元為工件 C3D8，(8-代碼是線性磚 )的元素。粗糙網(wǎng)格圖中約有 4000 個節(jié)點和 3343 個元素，精細網(wǎng)格圖中約有 7586 個節(jié)點和 6487 個元素。研究的基本條件包括：固定模具底部，模具底部所有節(jié)點的 U2=0，半月形模塊頂部受 200MPA，初期模數(shù)是

42、 200GPA，泊松比率是 0.3。為了分析裂紋 1 區(qū)域內(nèi)的主應力集中區(qū)要研究多個案例。 圖 3 中 a 和 b 兩個模型所展示的為案例 1，圖 3 中 C 圖新模型展示為案例 2，模具分成三個部分。使用有限元分析命令及接觸副連接分開的表面。 此模型的優(yōu)點在于易于改變半月形模塊的網(wǎng)格及其位置。首先，如圖 3 中 d 圖所示為案例 3，半月形模塊朝中心移到 6 毫米，然后，半月形- 7 -：蓋板零件的沖壓工藝及模具設(shè)計模塊內(nèi)圓角由 0 變?yōu)?0.5 毫米。3.2 結(jié)果和討論對于案例 1 中所使用的兩個網(wǎng)絡格，如圖 4 中 a 和 b 所示，最大主剪向力分布在圓角區(qū)內(nèi)。此結(jié)果顯示，兩個不同網(wǎng)格圖

43、受力區(qū)分布一樣。因此問題可以歸結(jié)為一個。埃爾頓及其合作者展示了模具頂端的軸形受力分析，在他們的研究中，當工件材料向下填充模具和圈之間的空間時，模具的接觸面拉長，在承轉(zhuǎn)半徑區(qū)域，主應力改變方向并且達到一個高的拉力。圖 3.（ a）粗網(wǎng)格（ b）細網(wǎng)格（ c）沖模網(wǎng)格的另一部分（ d）月牙形向中心移動（ e）月牙形不同變化的模式根據(jù)他們的分析，導致疲勞故障的原因有兩個：第一，當應力超出模具材質(zhì)的強度時，局部塑性區(qū)在第一次循環(huán)負載中漸漸產(chǎn)生，并且在接下來的重復負載中經(jīng)歷塑性區(qū)。因此，微小的裂紋產(chǎn)生。第二，主應力拉伸致使微小的裂紋產(chǎn)生并最終導致其擴大。圖 5 中 a 圖所示，馮米塞斯應力分布， 在半月

44、形模塊和內(nèi)圓區(qū)產(chǎn)生較高的應力。 加入接觸面壓力保持增長，塑性區(qū)在這兩個區(qū)域內(nèi)首先出現(xiàn)。圖 5 中 b 圖展示最大主應力分布。 為了展示裂紋 1 出現(xiàn)的區(qū)域， 圖 5 中 C 提供樂兒放大的受力圖。很明顯，在半月形模塊和自由邊之間存在25.5MPA 的里，這也是導致裂紋出現(xiàn)的原因。當裂紋增加至1-2 個格時，導致裂紋產(chǎn)生的應力必須與此平面平行。圖 5 中 b 圖顯示最大主應力在節(jié)點145 上的方向，此圖也確認了裂紋1 相當于 1-2 個點。圖 4.（a）網(wǎng)格物體在圓角處的最大主剪應力（b）細網(wǎng)格物體在圓角處的最大主剪應力圖5.應變應力分布反復撞擊后，裂紋2 出現(xiàn)在圓角區(qū)，因此而導致疲勞故障增加。

45、此研究中的區(qū)域與埃爾頓機器合作者所研究的非常相似。然而，當前問題中，此區(qū)域沒有接觸應力。圖 5 中 b 圖所示，在圓角區(qū)域最大的主應力都是收縮的。圖 5 中 e 圖所示，在圓角區(qū)有大約 30MPA 的剪應力。此剪應力好像是導致裂紋產(chǎn)生和擴大的原因。案例 1 至案例 4 的主力效果如表格 1。當半月形模塊的組成元素由 10 增至 70 時，裂紋中最大主應力增至（ 30.5-25.2）/30.5=10% (案例 2)，由此可見，最大主應力于半月形模塊息息相關(guān)。- 8 -案例 2 至去哪里 4，顯示半月形模塊的位置及其內(nèi)圓角的變化。如果半月形模塊向中心移動 6 毫米，裂紋 1 處產(chǎn)生的最大主應力減少

46、 （ 25.3-30.5）/30.5=-17% （案例 3）。如果半月形模塊內(nèi)圓角變成0.5 毫米，那么主應力減少（28.5-30.5）/30.5=-7%（案例 4）。因此，這兩種方法都可以減少應力集中。其中第一種效果更明顯。幾何圖形和內(nèi)圓角在模具應力分析上的作用 4.1 二維模擬為了羽化模具，提前討論幾何及其內(nèi)圓角在模具上大的應力作用。如圖6 中所示，使用軸形圖來分析。 首先設(shè)定內(nèi)圓 r1毫米，其高h=5毫米，外圓的高為H=25毫米，=10半徑 r2 為外圓半徑， r2/r1 的比率由 1.2變成 1.5、2.0、3.0 和 4.0，圓角的半徑 R 由 2.0毫米調(diào)至 0.5 毫米， h 由

47、 5 毫米換至 2 毫米和 0 毫米。模型頂部變成 200MPA，模具底部節(jié)點固定，其它自由轉(zhuǎn)換。 （除了在軸上的方向）圖 6.軸對稱的沖模型剖面4.2 結(jié)果和討論同過 30 個案例的研究，決定因素包括 r2 軸， h 內(nèi)圓角 R。 30 個案例研究如表2 所示，所有案例中， r1 固定為 10 毫米， H 固定為 25 毫米。圖 7. (a) r 2 / r1 =1.2,h=5mm,R=2mm;(b) r2 / r1 =1.5,h=5mm,R=2mm;(c) r2 / r1 =3.0,h=5mm,R=2mm;(d)r2 / r1 =1.2,h=2mm,R=2mm; (e) r2 / r1 =

48、1.2,h=2mm,R=2mm; (f) r2 / r1 =1.2,h=5mm,R=2mm4.2.1r2/r1 比率的作用設(shè)定 h=5 毫米的條件下，研究r2 1 的比率。如圖 7 中 a-c 所示， h 固定為 5 毫米，改變 r21 的比率，最大主應力隨 r2/r/r1 的增大而減小，位置上由上一個頂向下表面變化。/r這個趨勢如圖 8 中 a 所示。另一方面，圖 8 中 b 所示，最大剪應力隨著 r2/r1 的增大而變大。這種增加趨勢隨 r2/r1 的增加而降低，圖 7 中 f-h 顯示應力圖。h 的作用固定 R=2 毫米的前提下，對內(nèi)圓的高度 h 做變化，假定 h=0.2 毫米，如圖 8

49、 中 a 所示，最大主應力隨 h 增加， r2/r1=2, 有細微的增加。在此之后，趨勢有所變化。然而對于 h，其效果并不重要。另外，隨著 h 與 r2/r1 比率同輔增加，最大剪應力增加，應力模塊如圖 7 中 a-f I j 。內(nèi)圓角 R 的作用設(shè)定內(nèi)圓角 R=0.5 毫米和 2 毫米時，對其研究。結(jié)果如圖8 中 c 和 d 所示，通過圖- 9 -：蓋板零件的沖壓工藝及模具設(shè)計像所示，當 r2 1 大于 2 時，內(nèi)圓角區(qū)域內(nèi)最大主應力變化不大。當r2/r1 小于 2 時，內(nèi)圓/r角增大，主應力增大。然而，如圖 8 中 d 圖所示，與最大線性主應力相比，主應力的改變沒有那么大。如圖 8 中 d

50、 圖所示，當內(nèi)圓角半徑由 2 毫米到 0.5 毫米時（與 r2/r1 相同），最大線性力增加一倍。應力圖如圖 7 中 a f r i圖 8（a） r2 / r1 =1.2-4.0,h=0-5mm,R=2mm; (b)r2 / r1 =1.2-4.0,h=0-5mm,R=2mm; (c) r2 / r1=1.2-4.0,h=5mm,R=0.5 和 2mm;(d) r2/ r1 =1.2-4.0,h=5mm,R=0.5 和 2mm4.2.4 優(yōu)化方案建議通過以上分析，總結(jié)以下幾點建議。第一，最大主應力和最大剪應力隨著h 的增加而增加，因此h 應該相對小點。第二，隨著 R 的變化，最大主應力和最大剪應力的數(shù)值趨勢不同。如果最大主應力是導致模具失敗的潛在原因，那么 R 應該減小。相反，如果最大剪應力是潛在原因， R 的數(shù)值應該變大。一般來說， R 的數(shù)值在 1.5 毫米到 2.0 毫米之間。第三，當 r2/r1 小于 2 時， r2/r1 對最大主應力和最大剪應力影響深遠，然而趨勢不同。如果主應力是導致模具失敗的原因，r2/r1 的比