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中國地質(zhì)大學長城學院 本 科 畢 業(yè) 設 計外文文獻翻譯 系 別 工程技術(shù)系 學生姓名 陳東輝 專 業(yè) 機械設計制造及其自動化 學 號 05211523 指導教師 楊運強 職 稱 教授 2015年 4 月 20日 金屬正交切削中的殘余應力和壓力 摘要 在平面變形情況下，有限元法用于模仿和分析正交金屬切削過程。在剩余應力和張力領域完成制件與對焦。采用了各種建模。沿工具芯片界面摩擦相互作用，建模與改良庫侖摩擦法?；谂R界應力準則的節(jié)點釋放技術(shù)建立芯片分離模型。在與溫度相關(guān)的材料屬性和工具的范圍內(nèi)，確定是前角和摩擦系數(shù)的值。實驗發(fā)現(xiàn)通過熱冷卻，取決于這些參數(shù)的范圍可以增加殘余水平應力，傾角和磨擦系數(shù)的影響，并且是非線性的。比較預測殘余應力與文獻中的實驗觀測結(jié)果。 關(guān)鍵詞： 有限限元模擬 金屬正交切削 殘余應力 1.導言 金屬正交切削，非線性復雜耦合的熱機械進程的加工操作。應變和主剪切帶中的高應變率和相應芯片與工具之間的聯(lián)系，沿輔助剪切區(qū)域復雜性的摩擦。 除上述以外，工作形成的切屑和工具之間的摩擦引起產(chǎn)熱。在金屬切削加工的副產(chǎn)品中，出現(xiàn)殘余應力與新增壓力，會影響已加工表面的完整性，縮短機械組件蠕變疲勞壽命。因此，審慎評估工件殘余應力與應變的區(qū)域是必要的，針對機械零件在蠕變疲勞載荷條件下過早失效，要對切削過程的進行優(yōu)化與維護。 在過去60 年中，已經(jīng)進行了大量的金屬切削研究工作，Theearliest和 Piispanen 開發(fā)了金屬切削力學分析模型。這些模型被稱為剪角模型，它們都提供剪角、 傾角和磨擦系數(shù)的實證關(guān)系。這些模型還可用于估計部件、 應力和平面應變條件下的金屬切削加工過程中的能源消耗。在這以后制訂了更復雜的剪角模型，以包括各種設計參數(shù)的影響。Lee李和 Shaffer 提出一種基于滑移線場理論，其中假定剛性完美塑料材料切削和直剪切平面的剪角模型。kudo通過引入曲線的剪切平面來考慮控制曲線的切片和直線工具之間的接觸，修改滑移線模型。帕爾默.奧克斯利和奧克斯利認為是在粘塑性條件和工件硬化及應變率效應。duke等人研究芯片和工具之間的界面摩擦的安置，觸發(fā)器和分析局部加熱的金屬切削加工的影響。有限元方法已經(jīng)廣泛的應用于各種金屬切削技術(shù)的研究。有限元方法的多功能性使得它考慮到工件大變形、 應變率效應、 工具芯片接觸和摩擦，局部加熱和溫度的影響、 不同邊界和加載條件，和其他現(xiàn)象遇到的金屬切削加工問題。Usui和 Shirakashi 開發(fā)的金屬切削加工模型是早期有限元模型之一?；诮?jīng)驗數(shù)據(jù)，他們假定無關(guān)變形的材料和工具提示在芯片分離幾何的標準。巖田等人提議低速金屬切削的有限元模型，其中假定塑料為材料和包括該工具與芯片之間的摩擦的影響 （但忽略溫度影響）。Strenkowski 和卡羅爾，用基于在工件中有效的塑性應變芯片分離準則，更新了的拉格朗日制訂的代碼 NIKE2D 有限元。Komvopoulos 和 Erpenbeck 研究的各向同性的應變硬化和 strainrate研究的敏感性視為理想彈塑性材料和材料。有限元分析基于耦合熱彈塑性大變形本構(gòu)模型和雇用芯片分離的應變能量密度標準。田和楊上在正交的金屬切削過程，基于最優(yōu)理論和歐拉參考系統(tǒng)中的一個極限分析定理進行有限元研究。施和楊進行了兩個有限元正交金屬切削研究實驗 。通用有限元代碼的正交金屬切削研究和調(diào)查的摩擦影響和工具的形變場數(shù)量分布的傾角。已經(jīng)比較了這些研究與文獻中的實驗數(shù)據(jù)和新的測試及其作者所取得的成果。 以上討論的分析與數(shù)值提供了很好的金屬切削過程的理解與模擬的研究。尤其是，這些研究涉及大應變和應變率、 穩(wěn)態(tài)反應、 摩擦和局部加熱的影響和芯片分離標準等問題。但是，已進行的多計算工作，以了解有關(guān)機械加工零件的表面完整性的問題。 已知殘余應力會使表面完整性產(chǎn)生影響。Henriksen 為了解在加工表面的各種切削條件下的鋼和鑄鐵零件中的殘余應力進行一系列的測試。他在報告說殘余應力可能高達 689.48 MPa 。他還強調(diào)了在韌性材料 （如碳鋼） 。通常拉伸和壓縮的脆性材料 （鐵等）。由于各種原因已歸入在工件中的殘余應力的原因。劉和拉什觀察到工件表面的機械變形誘導殘余應力?？浦Z中南工業(yè)大學和 Tonsoff 等人發(fā)現(xiàn)殘余應力是依賴的切削速度，殘余應力對工件材料的硬度有重大影響。表明在金屬切削中的摩擦也有助于形成的殘余應力。確定了機械加工零件，如評價顯微硬度、 表面完整性的各種方法 x 射線衍射，和層去除偏轉(zhuǎn)技術(shù)。 日本早稻田大學柿野，發(fā)現(xiàn)殘余應力均與加工中的切削力和溫度分布有關(guān)，提出了早期預測模型的殘余應力。在另一種分析模型中，連接殘余應力和工件最脆弱部位。施和楊進行了機械加工的工件殘余應力分布的聯(lián)合實驗，計算研究。最近，劉和郭用有限元方法來評價在工件的殘余應力。他們還觀察到進行第二次下調(diào)時在切割面上殘余應力幅度降低了。 雖然現(xiàn)有的資料為機械加工部件的殘余應力的研究提供了重要的見解，但是殘余應變分布，從每個階段的切割冷卻過程中工具耙角影響的等問題，仍然沒有得到充分的理解。為此，這項調(diào)查的目的是要了解工具界面摩擦和工具耙角度對形成和分布的殘余應力和應變的機械加工零件是如何影響的，并劃分切割冷卻過程分為四個階段 并調(diào)查的每個階段的用處。有限元方法用于模擬正交金屬切削的過程，通過使用 ABAQUS 的通用代碼中的幾個高級的建模選項，制定了仿真程序。采用最新的拉格朗日制訂適合大應變變形。假定平面應變條件。包括電源過壓粘塑性本構(gòu)模型與應變率效應。沿工具芯片界面摩擦接觸已遵守修改庫侖摩擦定律。在絕熱加熱條件下，對可塑性和摩擦所致的局部加熱升溫?；趹Φ男酒蛛x建模標準把工件的芯片分離，被認為是依賴于溫度的物質(zhì)屬性。這項研究提供了詳細的博覽會的不同階段后切割、 應力、 應變場演化和形成的殘余應力和工件的成品表面附近的金相。 2.有限元模型描述 圖 1 顯示了金屬正交切削過程，是其中一個連續(xù)的芯片正在從工件切削刀具相對于工件勻速移動的原理圖。 在芯片分離和對待摩擦的交互工具-芯片-工件系統(tǒng)中，定義了三個相關(guān)關(guān)系。如圖 1 所示。接觸面1的切割路徑，兩個接觸表面由兩組節(jié)點 （每個面上一個） 粘合在一起并用配對。當達到芯片分離標準，工具提示的聯(lián)系節(jié)點距離，使該工具以增量方式推進。作為工具的聯(lián)系節(jié)點對材料成形芯片的內(nèi)面，將移動到所接觸面2的定義區(qū)域，和那些形成成品的工件表面將移動到接觸面3，如圖 1 所示。雖然有接觸面2的芯片和工具的前刀面之間的摩擦相互作用，接觸面3 只用于維護工具提示新切工件表面的接觸。 因為相比與平面維度的工件，被刀具切削的材料層的厚度通常是非常薄，聲稱是平面應變條件。由于其與芯片和工件的高剛度、 切割工具作為剛體理想化，建模的彈性材料與人工高楊氏模量 （2.1 × 1015 MPa 在此研究中使用的值）。 本節(jié)的其余部分描述了一些實施這項研究進行的金屬切削模擬計算要點。 2.1.摩擦界面 沿 toolchip 界面的接觸摩擦的影響，通過修改庫侖摩擦法 （在 ABAQUS 中可用的選項）建立模型，。它指出在一個聯(lián)系點的相對運動將發(fā)生是否應用抗剪應力 t 相切的聯(lián)系人界面到達下面定義的 tc 的臨界摩擦剪應力。 （1） 其中 p 是接觸點處的正常壓力、 n 是摩擦系數(shù)，t是閾值，剪應力。它指出，當t設置為無窮大時，常規(guī)的庫侖摩擦法收回。在此研究中，工件材料是 AISI 4340 鋼，這是略高于材料的屈服應力在簡單剪切。 圖1 金屬切割與相關(guān)部分 2.2.能量耗散和局部加熱 在金屬切削過程中，在芯片和工件的塑料工作和沿 toolchip 摩擦工作接口局部加熱造成的能量耗散。在高速切削，產(chǎn)生的熱量已沒有時間傳導和由此產(chǎn)生的溫度上升通常被視為工件自身承受。絕熱加熱條件下，局部溫度升高，Tp，誘導塑料工作在時間間隔 t，可以寫為 （2） J，相當于熱轉(zhuǎn)換因子，c 比熱、 密度，r 和塑料工作的百分比轉(zhuǎn)化為熱能的 hp （通常，85%hp 95%； hp = 90%在此研究中 [16,35])。 （3） 其中 t 是接觸點處的剪應力、 s˙ 是滑動速度，，J，c 和 r 是界定的智商系數(shù) hf 代表摩擦工作轉(zhuǎn)化為熱量，這作為這項研究的 1.0 的小數(shù)部分。沿工具芯片接口，產(chǎn)生的總熱量的一半 （50%） 假定走進芯片和另一半到工具。 2.3.芯片分離 在金屬切削加工仿真中，沿切削工具前小區(qū)域的應力和變形區(qū)域，芯片分離切割平面，滿足某些芯片分離的判據(jù)。值得注意的是研究表明芯片的幾何形狀和應力應變場的分布不影響。在本研究中，用于控制芯片分離的臨界應力，按照這一標準，在一定距離的工具提示之前到達一個關(guān)鍵的組合芯片分離時發(fā)生應力狀態(tài)。數(shù)學上，可以作為下面給定的應力索引 （4） 沿切割的路徑，剪切力和正常組件應力，工具提示指定距離處的應力狀態(tài)。如圖 1 所示是失去壓力下純材料的拉伸和剪切加載條件下切削。芯片分離發(fā)生時應力指數(shù) f 達到工具提示前一個元素長度 (在這項研究的約 50.8 μ m) 的值。對于AISI 4340材料鋼，臨界壓力也就是948 MPa 和 548 MPa （基于 von Mises 屈服的關(guān)系）。 2.4.材料模型 工件是 AISI 4340材料鋼在粘塑性本構(gòu)模型建模。 （5） 在一定電壓下進行適合高應變率應用程序 （如高速金屬切削）。標準的常量值用于其他物理屬性 （比熱 c = 502.0 J/動量K 和大規(guī)模密度 r = 7800 kg/m3)。在金屬切削加工過程中產(chǎn)生的巨大熱量將改變工件材料的材料特性。因此，依賴于溫度的材料屬性 (例如彈性常數(shù)、 初始屈服應力和熱膨脹系數(shù)） 。 2.5.有限元網(wǎng)格和邊界條件 圖 2 顯示了有限元離散化整個幾何模型的工件-芯片-工具系統(tǒng)。芯片層由傾斜的元素組成，它們從工件中分離，在交互的工具切割時，防止過度失真的元素。約 64 ° 的傾角的傾斜元素與切削方向。該芯片切割的起始位置，一層芯片的右端是最初分隔從工件，以便順利和快速過渡到穩(wěn)定狀態(tài)。左端，芯片層三角部分維持以使網(wǎng)格生成更簡單和不可望對穩(wěn)態(tài)仿真結(jié)果的影響。此網(wǎng)格設計是有效和原擬由 Strenkowski 和卡羅爾，并已經(jīng)通過其他研究人員的可肯定 圖 2 所示的有限元網(wǎng)格由 1160個四節(jié)點平面應變元素與 1308個節(jié)點組成。在預期大變形芯片中，網(wǎng)格的芯片圖層是比工件更精細。具體而言，芯片層，其中有 254 μ m 的高度 （切削深度），分為十個二類油層的元素。該工件區(qū)域，其中有 2540年 μ m 的長度和高度 889 μ m，分為 11 層，但每個有 50 個元素在切削方向。它被發(fā)現(xiàn) 50 個元素是使用頻譜-評價的有限元模擬，在切割工具到達左結(jié)尾之前以達到穩(wěn)定狀態(tài)。下方的切割路徑元素的頂部五層細是維度 50.8 μ m × 50.8 微米，這些是比工件網(wǎng)格的下半部分中的那些小方形內(nèi)容與離散化。 圖2 金屬切割網(wǎng)格層 工件邊界條件的指定方式如下：因為下半部分中的工件材料可望接受很小的變形，工件的底部邊界被認為具有零位移。由于工件是足夠長，在實現(xiàn) （忽略任何瞬變影響的開頭和末尾的切割模擬） 穩(wěn)態(tài)解的切割方向，左、 右兩端的工件邊界和切削方向被限制。 為了保持耙角度和剛性切割工具的間隙角，鑒于該工具是基長度407 μ m，高度 762 μ m 的平行四邊形的形狀。它由 60 大小相等平面應變元素組成。雖然該工具是在切割過程中與恒速負 x 方向移動，該工具的上邊緣是始終限制在 y 方向在整個切割過程中。在此研究中，n 的恒定的切削速度 = 2.54 m/s (為 152.4 米/分鐘） 。 Residual stresses and strains in orthogonal metal cutting C. Shet, X. Deng Department of Mechanical Engineering, University of South Carolina, Columbia, SC 29208, USA Received 7 August 2002; received in revised form 29 October 2002; accepted 3 January 2003 Abstract The nite element method is used to simulate and analyze the orthogonal metal cutting process under plane strain conditions, with focus on the residual stress and strain elds in the nished workpiece. Various modeling options have been employed. The frictional interaction along the tool-chip interface is modeled with a modied Coulomb friction law. Chip separation is modeled by the nodal release technique based on a critical stress criterion. Temperature-dependent material properties and a range of tool rake angle and friction coefcient values are considered. It is found that while thermal cooling increases the residual stress level, the effects of the rake angle and the friction coefcient are nonlinear and depend on the range of these parameters. The predicted residual stress results compare well with experimental observations available in the literature. 2003 Elsevier Science Ltd. All rights reserved. Keywords: Finite element simulation; Orthogonal metal cutting; Residual stress 1. Introduction Machiningoperations such as orthogonal metal cut- ting are complex nonlinear and coupled thermomechan- ical processes. The complexities are due to large strain and high strain-rate in the primary shear zone and due to the contact and friction between the chip and tool along the secondary shear zone. In addition to the above, complexities are also caused by local heat generation through the conversion of plastic work in the chip during chip formation and the frictional work between the tool and chip. An undesired byproduct of the metal cutting process is the creation of residual stresses and strains in the freshly cut workpiece, which is known to affect theintegrity of the newly nished surface, including short-ened creep and fatigue lives of the machined componentunder service loads. Hence a careful assessment of theresidual stress and strain elds in the workpiece is neces-sary for optimizing the cutting process and for safe-guarding against the premature failure of machined partsunder creep and fatigue loading conditions.A signicant amount of metal-cutting research workhas been carried out in the past 60 years. Amongst theearliest work were analytical models developed by Mer-chant [1,2] and Piispanen [3] on the mechanics of metalcutting. These models are known as the shear-anglemodels in that they provide empirical relations betweenthe shear angle, the rake angle and the coefcient offriction. These models can also be used to estimateforces, stresses, strains, and energy consumption in themetal cutting process under plane strain conditions.More sophisticated shear-angle models were laterdeveloped to include the effect of various design para-meters. Lee and Shaffer [4] proposed a shear-anglemodel based on the slip-line eld theory, which assumesa rigid-perfectly plastic material behavior and a straightshear plane. Kudo [5] modied the slip-line model byintroducing a curved shear plane to account for the con-trolled contact between curved chip and straight toolface. Palmer and Oxley [6] and Oxley et al. [7] con-sidered viscoplastic conditions and included work hard-ening and strain-rate effects. Doyle et al. [8] studied theeffect of interfacial friction between the chip and thetool. Trigger and Chao [9] analyzed the effect of localheating in metal cutting. Among the various numerical techniques for studyingmetal cutting, the nite element method has been widelyapplied. The versatility of the nite element methodallows it to take into account large deformation, strainrate effect, tool-chip contact and friction, local heating and temperature effect, different boundary and loading conditions, and other phenomena encountered in metal cutting problems. Usui and Shirakashi [10] developedone of the early nite element models for metal cuttingbased on empirical data. They assumed a rate-inde-pendent deformation behavior for the material and a geo-metric criterion for chip separation in front of tool tip.Iwata et al. [11] proposed a FEM model for low-speedmetal cutting, which assumed rigid-plastic behavior forthe material and included the effect of friction betweenthe tool and the chip (but ignored the temperature effect).Strenkowski and Carroll [12] used the general-purposenite element code NIKE2D with the updated Lagrang-ian formulation. They used a chip separation criterionbased on the effective plastic strain in the workpiece.Carroll and Strenkowski [13], and Strenkowski andMoon [14] also developed nite element models basedon the Eulerian formulation. Komvopoulos and Erpen-beck [15] considered elastic-perfectly plastic materialsand materials with isotropic strain hardening and strain-rate sensitivity. The nite element analysis by Lin andLin [16] was based on a coupled thermo-elastic-plasticconstitutive model with large deformation and employeda strain energy density criterion for chip separation.Tyan and Yang [17] conducted a nite element study onthe orthogonal metal cutting process based on a limitanalysis theorem in the context of an optimal theory andthe Eulerian reference system. Shih and Yang [18] andShih [19,20,21] carried out both experimental and niteelement studies on orthogonal metal cutting. Morerecently, Shet and Deng [22] and Shi et al. [23] studiedorthogonal metal cutting using a general-purpose niteelement code and investigated the effect of friction andtool rake angle on the distribution of thermomechanicaleld quantities. These studies have been compared withexperimental data in the literature and with new testresults obtained by their collaborators (see Deng andShet [24] and Zehnder et al. [25]). The analytical and numerical studies discussed above have provided a good understanding of the metal cuttingprocess. In particular, these studies have covered issuessuch as large strains and strain rates, the steady-stateresponse, the effect of friction and local heating and thechip separation criteria. It appears, however, that notmuch computational work has been carried out to under-stand issues relevant to the surface integrity ofmachined parts Residual stresses are known to cause poor surface integrity. Henriksen [26] conducted a series of tests to understand residual stresses in the machined surface of steel and cast iron parts under various cutting conditions. He reported that residual stresses could be as high as 689.48 MPa (100 ksi). He also found that residual stresses were usually tensile in ductile materials (e.g. carbon steel) and compressive in brittle materials (e.g. cast iron). Various reasons have been attributed to the cause of residual stresses in the workpiece. Liu and Bar- ash [27] observed that the mechanical deformation of the workpiece surface induced residual stresses. Kono et al. [28] and Tonsoff et al. [29] revealed that residual stresses are dependent on the cutting speed. Matsumoto et al. [30] and Wu and Matsumoto [31] observed that the hardness of the workpiece material has a signicant inuence on the residual stress eld. Konig et al. [32] showed that friction in metal cutting also contributes to the formation of residual stresses. Field et al. [33] reviewed various methods for determining the surface integrity of machined parts, such as micro-hardness evaluation, X-ray diffraction, and layer removal-deec- tion techniques. An early analytical model for predicting residual stresses was proposed by Okushima and Kakino [34], in which residual stresses were related to the cutting force and temperature distribution during machining. In another analytical model (Wu and Matsumoto [31]) a connection was made between residual stresses and the hardness of the workpiece. Shih and Yang [18] conduc- ted a combined experimental/computational study of the distribution of residual stresses in a machined workpiece. More recently, Liu and Guo [35] used the nite element method to evaluate residual stresses in a workpiece. They also observed that the magnitude of residual stress reduces when a second cut is made on the cut surface. While existing studies on residual stresses in machined parts have provided important insights, issues such as residual strain distributions, the effect of tool rake angle, the level of contribution from each stage of the cutting-cooling process, are still not well understood. To this end, the objective of this investigation is to understand how the tool-chip interfacial friction and the tool rake angle affect the formation and distribution of residual stresses and strains in machined parts, and div- ide the cutting-cooling process into four stages and investigate the contribution of each stage. The nite element method is used to simulate the orthogonal metal cutting process. A simulation procedure has been developed through the use of several advanced modeling options in the general-purpose code ABAQUS [36]. An updated Lagrangian formulation suitable for large strain deformations is employed. Plane strain conditions are assumed. Strain-rate effects are included with an over- stress viscoplastic constitutive model. Frictional contact along the tool-chip interface is made to obey a Modied Coulomb Friction Law. Adiabatic heating conditions are used to account for temperature rise due to local heating induced by plasticity and friction. Chip separation from the workpiece is modeled using a stress-based chip sep- aration criterion. Temperature-dependent material properties are considered. This study provides a detailed exposition of stress and strain eld evolution at different stages after cutting, and of the formation of residual stresses and strains near the nished surface of the work- piece. 2. Finite element model description Fig. 1 shows a schematic diagram of the orthogonal metal cutting process, in which a continuous chip is being taken off from the workpiece by a cutting tool that is moving relative to the workpiece with a constant velo- city In order to model chip separation and treat frictional interactions in the tool-chip-workpiece system, three contact pairs are dened, as shown in Fig. 1. Contact Pair 1 denes the cutting path, where the two contact surfaces are represented by two sets of nodes (one on each surface) that are paired and bonded together. When the chip separation criterion is satised, the contact node pair immediately ahead of the tool tip is separated, enabling the tool to advance incrementally. As the tool breaks the contact node pairs, materials forming the chip’s inner face will move into the region dened by Contact Pair 2, and those forming the nished work-piece surface will move into the region of Contact Pair 3, as illustrated in Fig. 1. While Contact Pair 2 models the frictional interaction between the chip and tool’s rake face, Contact Pair 3 is used only to maintain tool tip contact with the newly cut surface of the workpiece. Because the thickness of the layer of material being removed by the cutting tool is usually very thin com-pared to the out-of-plane dimension of the workpiece,the plane strain condition is claimed. Due to its highstiffness relative to the chip and workpiece, the cuttingtool is idealized as a rigid body and is modeled as anelastic material with an articially high Young’s modu-lus (a value of 2.1× 1015 MPa is used in this study).The rest of this section describes some of the keycomputational elements implemented in this study inorder to carry out the metal cutting simulations. 2.1. Interfacial friction To model the effect of contact friction along the tool-chip interface, a Modied Coulomb Friction Law (anoption available in ABAQUS) is adopted. It states thatrelative motion at a contact point will occur if theapplied shear stresst tangent to the contact interfacereaches the critical frictional shear stresstc dened below t c min( np,t th) (1) where p is the normal pressure at the contact point, n is the coefcient of friction, and t th is a threshold shear stress value. It is noted that, when t th is set to innity, the conventional Coulomb Friction Law is recovered. In this study, the workpiece material is AISI 4340 steel and t th is taken to be 549 MPa, which is slightly higher than the material’s yield stress in simple shear. 2.2. Energy dissipation and local heating In a metal cutting process local heating arises because of energy dissipation due to plastic work in the chip and workpiece and due to the frictional work along the tool- chip interface. In high-speed cutting, the heat generated has no time for conduction and the resulting temperature rise is usually considered to take place locally. Under the above adiabatic-heating conditions, the local temperature rise, T p, induced by plastic work in a time interval t, can be written as where s e is the effective stress, e ˙ p the effective plastic strain rate, J the equivalent heat conversion factor, c the specic heat, r the mass density, and 圖1 金屬切割與相關(guān)部分 Similarly, the local temperature rise T f caused by friction in a time interval t can be determined from 2.3. Chip separation In metal cutting simulations, chip separation along the cutting plane takes place when the stress and defor- mation states in a small region ahead of the tool tip satisfy a certain chip separation criterion. It is worth not- ing that the study by Huang and Black, [37] has shown that the geometry of the chip and the distribution of stress and strain elds are not very much inuenced by the use of a particular chip separation criterion. In the present study, a critical stress criterion is used to govern chip separation. According to this criterion, chip separ- ation occurs when the stress state at a certain distance ahead of the tool tip reaches a critical combination. Mathematically, this critical stress criterion can be writ- ten in terms of a stress index parameter f as given below where s n = max(s2,0)where t and sn are the shear andnormal stress components of the stress state at a specieddistance in front of the tool tip along the cutting path,as shown in Fig. 1, andsf and tf are the failure stressesof the material under pure tensile and shear loading con-ditions, respectively. Chip separation occurs when thestress index f reaches the value of 1.0 at one elementlength (approximately 50.8m in this study) ahead ofthe tool tip. For the material AISI 4340 steel, the failurestresses