AN UPPER BOUND SOLUTION FOR THE FORCE OF COMBINED BACKWARD-FORWARD EXTRUSION

A rigid-triangle velocity field for combined backward-forwardextrusion based on the experiments and the slip-line field isproposed in this paper.The flow separation point in the ri-gid-triangle velocity field is defined in accordance with theslip-line theory.A formula of minimum upper bound solutionfor the punch pressure of the combined extrusion is derived.The values from this formula are compared with those from theslip-line solution and with experimental results.The formulaof upper bound solution can be used in practice.     

ANALYSIS OF SURFACE CRACK ON FORWARD EXTRUDING BAR DURING AXISYMMETRIC CUP-BAR COMBINED EXTRUSION PROCESS

In this paper,the kinematically admissible velocity field with surface crack on forwardextruding bar is put forward during the axisymmetric cup-bar combined extrusion process,in accordance with the results of model experiments.On the basis of velocity field,the necessary condition for surface crack formation onthe forward extruding bar is derived,with the help of upper bound theorem and theminimum energy principle.Meanwhile,the relationships between surface crack formationand combination of reduction in area for the part of forward and backward extursions(εb,εf),relative residual thickness of billet(T/R_0),frictional factor(m)or relativeland length of ram and chamber(l_b/R_0,l_f/R_0)are calculated during the extrusion process.Therefore,whether the surface crack on forward exturding bar occurs can be predictedbefore extruding the lower-plasticity metals for axisymmetric cup-bar combined extrusionprocess.The analytical results agree very well with experimental results of aluminium alloyLY12 (ASTM2024)an     

变形-损伤耦合的起塑性恒压轴对称充模胀形的有限元模拟

采用大变形刚粘塑性有限元法模拟超塑性恒压轴对称充模胀形过程、分析了模具几何参数及材料参数对胀形过程中材料的流变行为、胀形制许厚度分布和成形时间的影响规律。给出了质点的流动轨迹、不同时刻制件的剖面形状及应力、应变分布；基于修正的Gurson粘塑性势推导了内部空洞体积分数累积增大模型并据此进行了变形-损伤耦合计算．     

Forming limit during superplastic deformation of sheet metals

ＦＯＲＭＩＮＧＬＩＭＩＴＤＵＲＩＮＧＳＵＰＥＲＰＬＡＳＴＩＣＤＥＦＯＲＭＡＴＩＯＮＯＦＳＨＥＥＴＭＥＴＡＬＳＤｕＺｈｉｘｉａｏ（杜志孝）;ＬｉＭｉａｏｑｕａｎ（李淼泉）;ＬｉｕＭａｂａｏ（刘马宝）;ＷｕＳｈｉｃｈｕｎ（吴诗惇）（Ｆａｃｕｌｔｙ４０２ｏ...     

Analysis of surface crack on forward extruding bar during axisymmetric cup-bar combined extrusion process

In this paper, the kinematically admissible velocity field with surface crack on forward extruding bar is put forward during the axisymmetric cup-bar combined extrusion process, in accordance with the results of model experiments.On the basis of velocity field, the necessary condition for surface crack formation on the forward extruding bar is derived, with the help of upper bound theorem and the minimum energy principle. Meanwhile, the relationships between surface crack formation and combination of reduction in area for the part of forward and backward extursions (ε_b,ε_f) relative residual thickness of billet (T/R₀),frictional factor (m) or relative land length of ram and chamber (l_b|R₀,l_f|R₀) are calculated during the extrusion process. Therefore, whether the surface crack on forward exturding bar occurs can be predicted before extruding the lower-plasticity metals for axisymmetric cup-bar combined extrusion process.The analytical results agree very well with experimental results of aluminium alloy LY12 (ASTM 2024) and LC4 (ASTM 7075).     

复合挤压力的上限解

本文根据实验和滑移线场拟定复合挤压时的速度不连续刚性三角形,由此得出复合挤压时凸模单位压力的最小上限解的解析式,将此式解值和实测值进行比较,表明上限值可供实际使用.