纳米尺度黏着接触和裂纹扩展的准连续介质方法研究
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摘要
研究纳米尺度下材料的特殊力学行为是一个涉及材料、物理等学科的复杂的课题。在这一尺度下,存在三个比较典型而富有意义的方向：(1)宏观尺度中未曾表现或可忽略的物理量,如材料的各向异性、黏着力、表面能成为影响材料和纳米器件的重要因素,研究这些因素对材料行为的影响变得极为重要。(2)材料科学中表征材料的参数,如堆垛层错能和孪晶能以怎样的方式影响和决定材料的变形机理并反映于材料的力学性质中。(3)宏观尺度下的连续介质理论在纳米尺度模型的适用性考察：连续介质模型什么尺度下仍然能适用?不适用的边界在哪里?
为了能尽可能的考察纳米尺度模型中出现的上述问题。我们采用准连续介质方法研究面心立方(FCC)或体心立方(BCC)金属的三个方面：镍(Ni)压头压入并拔出铜(Cu)基体的黏着接触行为和黏着接触各向异性行为；钽(Ta)的广义面错能和孪晶能及其对Ⅱ型裂纹尖端塑性变形机理的揭示；四种晶向选择下,具有初始裂纹的单晶钽(Ta)的裂纹扩展行为。通过这三个主题的研究发现：
(1)在黏着接触研究中,采用远大于分子动力学(MD)中的压头研究Ni压头和Cu基体的黏着接触。通过压深-载荷曲线和原子的组态的考察发现：压头压入和拔出体过程中,基体内部会形成一个非常大的塑性变形区。而且当压头完全拔出基体后,基体表面遭到严重破坏,基体深处仍然存有塑性变形。这表明纳米尺度的黏着作用对材料的破坏有非常大的影响；通过运用广义面错能曲线(GPF)发现单晶Cu形成孪晶层错结构需要克服的能垒(γutf-γsf)小于形成堆垛层错结构所需克服的不稳定堆垛层错能(γusf),这揭示了黏着接触过程中形变孪晶这一重要塑性变形产生的原因；黏着断裂中缩颈的断裂主要分为两种方式：压头回撤初期阶段的原子重排和末期阶段原子层沿易滑移面的剪切断裂；将模拟得到的黏着接触断裂的临界分离力(Fc)及临界半带宽(αc)和JKR理论值进行比较发现,两者存在偏差,模拟值是理论值的两倍左右。
(2)考察单晶钽(Ta)的(112)面沿[111]方向滑移时的广义堆垛层错能和广义孪晶能曲线发现：广义堆垛层错能曲线不存在能量极小值,这表明Ta内部不会形成单层的堆垛层错结构,位错只能以全位错形式发射；不同厚度的广义孪晶能曲线表明四个原子层的孪晶是亚稳定的,五层的孪晶是比较稳定的稳定孪晶；通过单晶Ta的Ⅱ型裂纹尖端的初始塑性变形研究发现,形变孪晶的产生和全位错的发射是裂纹尖端同时共存的两种塑性变形机理。裂纹尖端的初次塑性变形形成四个原子层厚的孪晶,随后迅速扩展为五层以至更高层。此外还发现全位错沿[111]晶向向裂纹尖端的前方发射。裂纹尖端的塑性变形验证了广义层错能曲线和广义孪晶能曲线能够较好地揭示了全位错和多原子层孪晶的产生。
(3)对四种晶向下具有初始裂纹的单晶Ta的Ⅰ型加载过程研究发现,四种晶向的裂纹表现出不同的脆塑性断裂机理：(Ⅰ)晶向为x[010],y[100]和z[001]时,裂纹所在的面具有较大的表面能,裂纹前方没有易滑移面,初始裂纹由初始时具有较大表面能的裂纹面转移到表面能较小的(110)面,但是裂纹扩展以脆性形式为主。(Ⅱ)晶向为x[110]，y[110]和z[001]时,裂纹所在面具有较小的表面能,裂纹前方没有易滑移面,应力强度因子为2.41K*Ic时初始裂纹沿原裂纹面脆性扩展。(Ⅲ)x[100],y[011]和z[011]时,裂纹所在面具有较小表面能,但裂纹前方具有易滑移面。裂纹扩展时裂纹尖端通过沿[111]和[111]方向发射全位错的形式使得裂纹尖端钝化。裂纹的钝化进一步导致裂纹尖端产生明显的相变,BCC形式的晶格排列转化为更加稳定的HCP形式,进一步抑制了裂纹的扩展。(Ⅳ)x[110],y[001]和z[110]时,裂纹在3.29K*Ic发生初次塑性变形。在这一晶向下,形变孪晶是裂纹尖端最主要的塑性变形形式,裂纹前方形成了较长的孪晶带,且随着加载孪晶带逐渐变宽。模拟发现裂纹大致沿着孪晶界的方向扩展。
(4)针对裂纹尖端四种不同的塑性和脆性断裂形式,提出利用变量ξ作为判定裂纹脆性还是塑性扩展的主要依据。这一变量一方面和初始裂纹所在面的表面能及位错发射的不稳定堆垛层错能有关,另一方面还与易滑移方向(位错发射方向)与裂纹尖端方向有关。ξ越大,裂纹就以脆性扩展为主；ξ越小时,裂纹倾向于伴随全位错或形变孪晶形式的塑性扩展。模拟结果证实了这一裂纹脆塑性扩展判定准则的正确性。
Studying the special mechanical behavior of nano-scale materials is a complex task that involves the displine of material and physical science. There are three typical and meaningful areas of research in nanoscale. First, mechanical behavior of nano-scale material is quite distinguishive from marco-scale material as a result of anisotropy, adhesive force and the surface energy. These factors are of great importance for the study of nano-scale devices. Sencond, In what way do some material parameters such as the stacking fault energy and the twinning fault energy influence or determine the deformation mechanism of materials. What is the connection between these parameters and mechanical behavior? Third, are some models for marco-scale under the assumption of continnum still suitable for nano-scale models? If not, where is the boundary between applicable and not applicable?
In order to shed some light on these three interesting and challenging issues, we study three aspects of FCC or BCC materials using the quasicontinnum method. We first study indentation and retraction processes between Ni indenter and Cu substrate. We also focus on the anisotropic behavior of noncontact between Ni indenter and Cu substrate. Second, the generalized stacking fault (GSF) and the generalized twinning fault energy (GTF) are investigated to reveal deformation mechanism of mode II type crack tip of BCC metal tantalum (Ta). Third, we make a detailed research on the different deformation mechanism of mode I type crack tip of Ta crystal under four different crystal orientations. Through careful study we find that:
A tip with a radius much larger than those used in MD is chosen to study nanocontact. By examing atomic configurations and the load-depth curve, a large plastic zone is observed during indentation and retraction processes. After deep neck facture, the surface of Cu substrate is severely damaged and plastic deformation in the Cu substrate does not disappear completely.This implies that strong adhesive force might lead to the damage of materials or nano-scale devices during nanocontact. The GPF curve of Cu reveals that the energy barrier (γutf-γsf) required for deformation twinning is smaller than the energy barrierγusf required for the formation of stacking fault. Therefore, deformation twinning tends to be one of the dominant deformation mechanism duing nanocontact. Two different fracture mechanisms are responsible for load jump at different stages. At the initial stage, fracture occurs by atomic rearrangement. As neck elongates, fracture occurs in the middle of Cu neck. Homogeneous shear along one (111) plane over another is the dominant fracture mechanism.Comparing the critical adhesive force (Fc) and the critical contact radius (ac)for Cu neck fracture with JKR model, we find that there is deviation existing between theoretical values and numerical results. The simulation results are roughtly two times larger than the theoretical results.
The generalized planar fault energy, including the generalized stacking fault (GSF) and the generalized twinning fault energy (GTF) of BCC metal tantalum (Ta) are investigated. The GSF of Ta reveals that no evident energy minimum is observed in the energy curve. This implies that full dislocations emitt on {112} slip plane rather than partical dislocations. The GTF predicts that the minimum thickness of a metastable twin is four layers and five layered twin is more stable. The incipient twin Ta tends to grow thick once it comes into being. To confirm the significance of the GSF and GTF in revealing incipient plasticity, plastic deformation of crackt tip of single Ta crystal under modeⅡloading is investigated. The results shows that deformation twin and full dislocation along <111> direction on {112} plane are two co-existent mechanisms of crack tip plastic deformation of Ta. The initial four layered twin quickly extends into five layers and much more layers with further loading. A full dislocation emitted into the front of the crack tip on {112} plane. These two plastic deformation mechanisms are well explained by the GTF and the GSF respectively.
The deformation mechanisms of initial crack propagation of Ta crystal orientated in four different ways are examined under load modeⅡ. The results distinguish from each other surprisingly. (1) In the case of x[010], y[100] and z[0 01], the initial crack plane has high surface and there are no slip planes. Therefore, the crack changes its original direction and extends in a brittle manner on (110) plane which has a lower surface energy. (2) In the case of x[110],y[110] and z[00 1], no slip plane is available in the front of crack tip and the initial crack plane has low surface. The crack propagagtes along its original plane brittlely when the stress intensity factor is 2.41 K*1c. (3) For the case of x[100], y[011]and z[011], there are two slip planes in the front of crack tip. The crack tip is blunded as two full dislocations are emitted in the direction of [111] and[111]. The effect of blunting is further strengthened by phrase transformation near the crack tip. It is much more difficult for crack to propagate ans the BCC lattice changes into HCP at the crack tip in this case. (4) In the last cases of x[110], y[001]and z[110], the first plastic deformation occurs at 3.29K*1c-Deformation twinning is the most important way of plastic deformation near crack tip. The twinning band becomes wider as load continues and the crack tends to propagate along the grain boundary.
Based on the four different way of crack propagation, a parameterξis proposed as the criterion of brittle or ductile fracture. The parameter is not only related with the surface enery of initial crack plane and unstable stacking fault energy but also related with the direction of slip plane. The largerξis, the much likely crack will propagate brittlely. The smallerξis, the crack will propagate in a ductile manner. Our simulation results confirm the validity of the criterion.
为了能尽可能的考察纳米尺度模型中出现的上述问题。我们采用准连续介质方法研究面心立方(FCC)或体心立方(BCC)金属的三个方面：镍(Ni)压头压入并拔出铜(Cu)基体的黏着接触行为和黏着接触各向异性行为；钽(Ta)的广义面错能和孪晶能及其对Ⅱ型裂纹尖端塑性变形机理的揭示；四种晶向选择下,具有初始裂纹的单晶钽(Ta)的裂纹扩展行为。通过这三个主题的研究发现：
(1)在黏着接触研究中,采用远大于分子动力学(MD)中的压头研究Ni压头和Cu基体的黏着接触。通过压深-载荷曲线和原子的组态的考察发现：压头压入和拔出体过程中,基体内部会形成一个非常大的塑性变形区。而且当压头完全拔出基体后,基体表面遭到严重破坏,基体深处仍然存有塑性变形。这表明纳米尺度的黏着作用对材料的破坏有非常大的影响；通过运用广义面错能曲线(GPF)发现单晶Cu形成孪晶层错结构需要克服的能垒(γutf-γsf)小于形成堆垛层错结构所需克服的不稳定堆垛层错能(γusf),这揭示了黏着接触过程中形变孪晶这一重要塑性变形产生的原因；黏着断裂中缩颈的断裂主要分为两种方式：压头回撤初期阶段的原子重排和末期阶段原子层沿易滑移面的剪切断裂；将模拟得到的黏着接触断裂的临界分离力(Fc)及临界半带宽(αc)和JKR理论值进行比较发现,两者存在偏差,模拟值是理论值的两倍左右。
(2)考察单晶钽(Ta)的(112)面沿[111]方向滑移时的广义堆垛层错能和广义孪晶能曲线发现：广义堆垛层错能曲线不存在能量极小值,这表明Ta内部不会形成单层的堆垛层错结构,位错只能以全位错形式发射；不同厚度的广义孪晶能曲线表明四个原子层的孪晶是亚稳定的,五层的孪晶是比较稳定的稳定孪晶；通过单晶Ta的Ⅱ型裂纹尖端的初始塑性变形研究发现,形变孪晶的产生和全位错的发射是裂纹尖端同时共存的两种塑性变形机理。裂纹尖端的初次塑性变形形成四个原子层厚的孪晶,随后迅速扩展为五层以至更高层。此外还发现全位错沿[111]晶向向裂纹尖端的前方发射。裂纹尖端的塑性变形验证了广义层错能曲线和广义孪晶能曲线能够较好地揭示了全位错和多原子层孪晶的产生。
(3)对四种晶向下具有初始裂纹的单晶Ta的Ⅰ型加载过程研究发现,四种晶向的裂纹表现出不同的脆塑性断裂机理：(Ⅰ)晶向为x[010],y[100]和z[001]时,裂纹所在的面具有较大的表面能,裂纹前方没有易滑移面,初始裂纹由初始时具有较大表面能的裂纹面转移到表面能较小的(110)面,但是裂纹扩展以脆性形式为主。(Ⅱ)晶向为x[110]，y[110]和z[001]时,裂纹所在面具有较小的表面能,裂纹前方没有易滑移面,应力强度因子为2.41K*Ic时初始裂纹沿原裂纹面脆性扩展。(Ⅲ)x[100],y[011]和z[011]时,裂纹所在面具有较小表面能,但裂纹前方具有易滑移面。裂纹扩展时裂纹尖端通过沿[111]和[111]方向发射全位错的形式使得裂纹尖端钝化。裂纹的钝化进一步导致裂纹尖端产生明显的相变,BCC形式的晶格排列转化为更加稳定的HCP形式,进一步抑制了裂纹的扩展。(Ⅳ)x[110],y[001]和z[110]时,裂纹在3.29K*Ic发生初次塑性变形。在这一晶向下,形变孪晶是裂纹尖端最主要的塑性变形形式,裂纹前方形成了较长的孪晶带,且随着加载孪晶带逐渐变宽。模拟发现裂纹大致沿着孪晶界的方向扩展。
(4)针对裂纹尖端四种不同的塑性和脆性断裂形式,提出利用变量ξ作为判定裂纹脆性还是塑性扩展的主要依据。这一变量一方面和初始裂纹所在面的表面能及位错发射的不稳定堆垛层错能有关,另一方面还与易滑移方向(位错发射方向)与裂纹尖端方向有关。ξ越大,裂纹就以脆性扩展为主；ξ越小时,裂纹倾向于伴随全位错或形变孪晶形式的塑性扩展。模拟结果证实了这一裂纹脆塑性扩展判定准则的正确性。
Studying the special mechanical behavior of nano-scale materials is a complex task that involves the displine of material and physical science. There are three typical and meaningful areas of research in nanoscale. First, mechanical behavior of nano-scale material is quite distinguishive from marco-scale material as a result of anisotropy, adhesive force and the surface energy. These factors are of great importance for the study of nano-scale devices. Sencond, In what way do some material parameters such as the stacking fault energy and the twinning fault energy influence or determine the deformation mechanism of materials. What is the connection between these parameters and mechanical behavior? Third, are some models for marco-scale under the assumption of continnum still suitable for nano-scale models? If not, where is the boundary between applicable and not applicable?
In order to shed some light on these three interesting and challenging issues, we study three aspects of FCC or BCC materials using the quasicontinnum method. We first study indentation and retraction processes between Ni indenter and Cu substrate. We also focus on the anisotropic behavior of noncontact between Ni indenter and Cu substrate. Second, the generalized stacking fault (GSF) and the generalized twinning fault energy (GTF) are investigated to reveal deformation mechanism of mode II type crack tip of BCC metal tantalum (Ta). Third, we make a detailed research on the different deformation mechanism of mode I type crack tip of Ta crystal under four different crystal orientations. Through careful study we find that:
A tip with a radius much larger than those used in MD is chosen to study nanocontact. By examing atomic configurations and the load-depth curve, a large plastic zone is observed during indentation and retraction processes. After deep neck facture, the surface of Cu substrate is severely damaged and plastic deformation in the Cu substrate does not disappear completely.This implies that strong adhesive force might lead to the damage of materials or nano-scale devices during nanocontact. The GPF curve of Cu reveals that the energy barrier (γutf-γsf) required for deformation twinning is smaller than the energy barrierγusf required for the formation of stacking fault. Therefore, deformation twinning tends to be one of the dominant deformation mechanism duing nanocontact. Two different fracture mechanisms are responsible for load jump at different stages. At the initial stage, fracture occurs by atomic rearrangement. As neck elongates, fracture occurs in the middle of Cu neck. Homogeneous shear along one (111) plane over another is the dominant fracture mechanism.Comparing the critical adhesive force (Fc) and the critical contact radius (ac)for Cu neck fracture with JKR model, we find that there is deviation existing between theoretical values and numerical results. The simulation results are roughtly two times larger than the theoretical results.
The generalized planar fault energy, including the generalized stacking fault (GSF) and the generalized twinning fault energy (GTF) of BCC metal tantalum (Ta) are investigated. The GSF of Ta reveals that no evident energy minimum is observed in the energy curve. This implies that full dislocations emitt on {112} slip plane rather than partical dislocations. The GTF predicts that the minimum thickness of a metastable twin is four layers and five layered twin is more stable. The incipient twin Ta tends to grow thick once it comes into being. To confirm the significance of the GSF and GTF in revealing incipient plasticity, plastic deformation of crackt tip of single Ta crystal under modeⅡloading is investigated. The results shows that deformation twin and full dislocation along <111> direction on {112} plane are two co-existent mechanisms of crack tip plastic deformation of Ta. The initial four layered twin quickly extends into five layers and much more layers with further loading. A full dislocation emitted into the front of the crack tip on {112} plane. These two plastic deformation mechanisms are well explained by the GTF and the GSF respectively.
The deformation mechanisms of initial crack propagation of Ta crystal orientated in four different ways are examined under load modeⅡ. The results distinguish from each other surprisingly. (1) In the case of x[010], y[100] and z[0 01], the initial crack plane has high surface and there are no slip planes. Therefore, the crack changes its original direction and extends in a brittle manner on (110) plane which has a lower surface energy. (2) In the case of x[110],y[110] and z[00 1], no slip plane is available in the front of crack tip and the initial crack plane has low surface. The crack propagagtes along its original plane brittlely when the stress intensity factor is 2.41 K*1c. (3) For the case of x[100], y[011]and z[011], there are two slip planes in the front of crack tip. The crack tip is blunded as two full dislocations are emitted in the direction of [111] and[111]. The effect of blunting is further strengthened by phrase transformation near the crack tip. It is much more difficult for crack to propagate ans the BCC lattice changes into HCP at the crack tip in this case. (4) In the last cases of x[110], y[001]and z[110], the first plastic deformation occurs at 3.29K*1c-Deformation twinning is the most important way of plastic deformation near crack tip. The twinning band becomes wider as load continues and the crack tends to propagate along the grain boundary.
Based on the four different way of crack propagation, a parameterξis proposed as the criterion of brittle or ductile fracture. The parameter is not only related with the surface enery of initial crack plane and unstable stacking fault energy but also related with the direction of slip plane. The largerξis, the much likely crack will propagate brittlely. The smallerξis, the crack will propagate in a ductile manner. Our simulation results confirm the validity of the criterion.
引文
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