压载荷对铝合金疲劳裂纹扩展影响的有限元建模及实验研究
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摘要
在进入21世纪的今天,随着断裂力学、损伤力学的深入研究,人们对传统的静载、无缺陷材料强度的认识已相当深刻,因此,疲劳成为导致金属零、构件失效的主要因素之一。对于航空航天领域广泛使用的铝合金材料,其疲劳寿命主要是裂纹稳定扩展寿命,因此,如何准确预报铝合金疲劳裂纹在实际载荷下的稳定扩展寿命是工程中必需解决的问题。但是,长期以来,通常认为疲劳裂纹在压载荷的作用下会导致闭合,裂纹不扩展,从而忽略压载荷对疲劳裂纹扩展寿命的影响,而已有的研究表明,疲劳载荷谱中的压载荷对金属疲劳裂纹的扩展是有影响的,对于铝合金材料,压载荷对裂纹扩展有促进作用,忽略其影响是危险的。因此,研究压载荷对铝合金疲劳裂纹扩展的影响具有很大的工程实用价值。
疲劳裂纹扩展寿命问题十分复杂,难以建立解析的、普遍的寿命预测模型,因此,用有限元模型模拟疲劳裂纹扩展的方法广泛地使用在疲劳研究中,有限元方法可以大大节省试验成本,缩短研究周期。通过对铝合金材料疲劳裂纹形成和扩展机理的研究可知,裂纹的形成和扩展与裂尖附近材料的塑性变形紧密相关,裂尖附近的材料在疲劳载荷作用下发生塑性变形,远离裂尖的材料只有弹性变形。依据裂尖附近材料的不同力学响应,结合弹塑性力学和断裂力学的相关理论和公式,建立可描述铝合金疲劳裂纹裂尖参数变化的二维静态弹塑性有限元模型。经过对动态疲劳与静态疲劳裂纹模型相比较,同时比较三维与二维疲劳裂纹模型可知,二维静态弹塑性有限元模型计算的结果是保守的,符合工程精度要求的,建模方法简单,计算高效,适合工程应用。
本文通过对裂尖应力、裂纹张开位移、等效塑性应变和裂尖前方塑性区尺寸等参数的弹塑性有限元结果的分析,验证了疲劳载荷中的压载荷对铝合金疲劳裂纹扩展的促进作用,得出材料的破坏主要集中在裂尖前1μm内的结论。在预报铝合金疲劳寿命时,其影响不可忽略。并且利用有限元计算结果,重新定义了新参数一有效应力强度因子范围ΔK′_(eff),建立了以ΔK′_(eff)为扩展参数的可定量描述在R=0～-1条件下铝合金疲劳裂纹稳定扩展的模型,结合铝合金疲劳裂纹扩展机理,分析了参数ΔK′_(eff)的工程合理性。经7049-UA和2A12-T4铝合金材料的实验数据验证,以AK'eff为扩展参数的模型与以K_(max)、ΔK、或K_(eff)作为扩展参数的模型相比较,能够更准确地反映出压应力对铝合金疲劳裂纹扩展的影响,预报的疲劳寿命是偏安全的。
由于高频疲劳试验机薄板试件夹具的刚度对试验的频率和试验的精度有很大影响,因此,本文利用有限元方法对高频疲劳实验机薄板试件夹具的联接结构进行了模态分析,分析结果表明,选用圆弧凹槽结构联接的夹具整体刚度较高;同时圆弧凹槽的半径和对夹具与试验机联接的螺纹长度对夹具的整体刚度都有影响,圆弧凹槽半径的合理范围应在(0.17～0.25)倍的板厚之间,螺纹长度的合理范围应在(1.43～1.55)倍的螺纹公称直径之间,此外还需要考虑螺纹副的自锁性和耐磨性来合理确定螺距。经实验检验,满足高频疲劳试验的要求。
Today, traditional strength design of static loading condition and non-defects material has been studied deeply with the development of fracture mechanics and damage mechanics. So the fatigue has become one of the main factors which induced failure of metal components. The aluminum alloy is used in aviation field widely and its fatigue life is crack steady propagation life. So, it is a big engineering problem to predict the real propagation life accurately of aluminum alloy under applied fatigue loading. But the knowledge of fatigue crack can not grow under compressive loading for the closure of crack for a long time. The compressive stress will be omitted in the fatigue strength design. From the research result, it has been found that the compressive stress affects fatigue crack propagation of metal materials. For the aluminum alloy, it is very dangerous to ignore it. Compressive stress promotes crack growth. So, the study of the effects of compressive stress on crack growth in the aluminum alloy under tensile-compressive loading spectrum will satisfy engineering application.
Neither analytical nor universal models have been found, because of the complexity of fatigue life. Now, finite element method is used widely in modeling fatigue crack growth. It is a good way to cut down the cost of fatigue test and shorten the period of fatigue study. From the mechanism research of aluminium alloy fatigue crack initiation and propagation, we know that crack initiation and propagation is closely connected to the plastic deformation in front of the crack tip. The plastic deformation which caused by the fatigue loading is adjacent to the crack tip. However, the elastic deformation occurred away from crack tip. According to the different mechanical responses of materials around crack tip, combined with the expressions of the elastic-plastic mechanics and the fracture mechanics, a two-dimensional static elastic-plastic finite element model which describe the change of the aluminium alloy crack tip mechanical parameters has been set up. Through the comparison of the difference and similar between static crack model and dynamic crack model, as well as the 2D model and 3D model at the same time, the computation results of two dimensional static elastic-plastic finite element model are conservative. It is a simple modeling method with high calculation efficiency, and suits for engineering application.
After analyzing elastic-plastic finite element results, such as crack tip stress analysis, crack opening displacement analysis, equivalent plastic strain analysis and the analysis of plastic zone size in front of the crack tip, it proved that compressive loading promoted crack growth in aluminium alloy, and the effects mainly occurred in the zone beyond crack tip less than 1μm. It is dangerous to neglect the effects of compressive loading when predicting fatigue life of aluminium alloy. Based on the finite element analysis results, a new parameter has been redefined, named effective stress intensive factor range-△K'_(eff). Based on this new parameter, a model has been set up which can calculate the fatigue crack propagation rate of aluminium alloy under stress ratio R=0～-1. According to the fatigue crack growth mechanism of aluminium alloy, engineering rationality of△K'_(eff) has been analyzed. The test datum of aluminium alloys 7049-UA and 2A12-T4 have been verified that the model based on the parameter△K'_(eff) can accurately described the effects of compressive stress on fatigue crack propagation of aluminium alloy. Compared with the computation results of the model based propagation parameter K_(max),△K, and K_(eff), fatigue life predicted by the model based parameter△K'_(eff) is safer.
Rigidity of plate specimen fixture used on the high frequency fatigue test machine can deeply affect the test frequency and test precision. So, we analyzed the joining structure of the plate specimen fixture by the finite element method. The analysis results showed that the whole rigidity of fixture with circular groove joining structures is higher than those of other types of joining structure, the radius of circular groove and screw length connecting the fixture and test machine are also affect whole rigidity. The reasonable magnitude of circular groove radius is about (0.17-0.25) times of the board thickness, and screw length is about (1.43-1.55) times of screw nominal diameter, furthermore, the reasonable magnitude of screw pitch determined by self-locking performance and wear resistance of screw pairs.
疲劳裂纹扩展寿命问题十分复杂,难以建立解析的、普遍的寿命预测模型,因此,用有限元模型模拟疲劳裂纹扩展的方法广泛地使用在疲劳研究中,有限元方法可以大大节省试验成本,缩短研究周期。通过对铝合金材料疲劳裂纹形成和扩展机理的研究可知,裂纹的形成和扩展与裂尖附近材料的塑性变形紧密相关,裂尖附近的材料在疲劳载荷作用下发生塑性变形,远离裂尖的材料只有弹性变形。依据裂尖附近材料的不同力学响应,结合弹塑性力学和断裂力学的相关理论和公式,建立可描述铝合金疲劳裂纹裂尖参数变化的二维静态弹塑性有限元模型。经过对动态疲劳与静态疲劳裂纹模型相比较,同时比较三维与二维疲劳裂纹模型可知,二维静态弹塑性有限元模型计算的结果是保守的,符合工程精度要求的,建模方法简单,计算高效,适合工程应用。
本文通过对裂尖应力、裂纹张开位移、等效塑性应变和裂尖前方塑性区尺寸等参数的弹塑性有限元结果的分析,验证了疲劳载荷中的压载荷对铝合金疲劳裂纹扩展的促进作用,得出材料的破坏主要集中在裂尖前1μm内的结论。在预报铝合金疲劳寿命时,其影响不可忽略。并且利用有限元计算结果,重新定义了新参数一有效应力强度因子范围ΔK′_(eff),建立了以ΔK′_(eff)为扩展参数的可定量描述在R=0～-1条件下铝合金疲劳裂纹稳定扩展的模型,结合铝合金疲劳裂纹扩展机理,分析了参数ΔK′_(eff)的工程合理性。经7049-UA和2A12-T4铝合金材料的实验数据验证,以AK'eff为扩展参数的模型与以K_(max)、ΔK、或K_(eff)作为扩展参数的模型相比较,能够更准确地反映出压应力对铝合金疲劳裂纹扩展的影响,预报的疲劳寿命是偏安全的。
由于高频疲劳试验机薄板试件夹具的刚度对试验的频率和试验的精度有很大影响,因此,本文利用有限元方法对高频疲劳实验机薄板试件夹具的联接结构进行了模态分析,分析结果表明,选用圆弧凹槽结构联接的夹具整体刚度较高;同时圆弧凹槽的半径和对夹具与试验机联接的螺纹长度对夹具的整体刚度都有影响,圆弧凹槽半径的合理范围应在(0.17～0.25)倍的板厚之间,螺纹长度的合理范围应在(1.43～1.55)倍的螺纹公称直径之间,此外还需要考虑螺纹副的自锁性和耐磨性来合理确定螺距。经实验检验,满足高频疲劳试验的要求。
Today, traditional strength design of static loading condition and non-defects material has been studied deeply with the development of fracture mechanics and damage mechanics. So the fatigue has become one of the main factors which induced failure of metal components. The aluminum alloy is used in aviation field widely and its fatigue life is crack steady propagation life. So, it is a big engineering problem to predict the real propagation life accurately of aluminum alloy under applied fatigue loading. But the knowledge of fatigue crack can not grow under compressive loading for the closure of crack for a long time. The compressive stress will be omitted in the fatigue strength design. From the research result, it has been found that the compressive stress affects fatigue crack propagation of metal materials. For the aluminum alloy, it is very dangerous to ignore it. Compressive stress promotes crack growth. So, the study of the effects of compressive stress on crack growth in the aluminum alloy under tensile-compressive loading spectrum will satisfy engineering application.
Neither analytical nor universal models have been found, because of the complexity of fatigue life. Now, finite element method is used widely in modeling fatigue crack growth. It is a good way to cut down the cost of fatigue test and shorten the period of fatigue study. From the mechanism research of aluminium alloy fatigue crack initiation and propagation, we know that crack initiation and propagation is closely connected to the plastic deformation in front of the crack tip. The plastic deformation which caused by the fatigue loading is adjacent to the crack tip. However, the elastic deformation occurred away from crack tip. According to the different mechanical responses of materials around crack tip, combined with the expressions of the elastic-plastic mechanics and the fracture mechanics, a two-dimensional static elastic-plastic finite element model which describe the change of the aluminium alloy crack tip mechanical parameters has been set up. Through the comparison of the difference and similar between static crack model and dynamic crack model, as well as the 2D model and 3D model at the same time, the computation results of two dimensional static elastic-plastic finite element model are conservative. It is a simple modeling method with high calculation efficiency, and suits for engineering application.
After analyzing elastic-plastic finite element results, such as crack tip stress analysis, crack opening displacement analysis, equivalent plastic strain analysis and the analysis of plastic zone size in front of the crack tip, it proved that compressive loading promoted crack growth in aluminium alloy, and the effects mainly occurred in the zone beyond crack tip less than 1μm. It is dangerous to neglect the effects of compressive loading when predicting fatigue life of aluminium alloy. Based on the finite element analysis results, a new parameter has been redefined, named effective stress intensive factor range-△K'_(eff). Based on this new parameter, a model has been set up which can calculate the fatigue crack propagation rate of aluminium alloy under stress ratio R=0～-1. According to the fatigue crack growth mechanism of aluminium alloy, engineering rationality of△K'_(eff) has been analyzed. The test datum of aluminium alloys 7049-UA and 2A12-T4 have been verified that the model based on the parameter△K'_(eff) can accurately described the effects of compressive stress on fatigue crack propagation of aluminium alloy. Compared with the computation results of the model based propagation parameter K_(max),△K, and K_(eff), fatigue life predicted by the model based parameter△K'_(eff) is safer.
Rigidity of plate specimen fixture used on the high frequency fatigue test machine can deeply affect the test frequency and test precision. So, we analyzed the joining structure of the plate specimen fixture by the finite element method. The analysis results showed that the whole rigidity of fixture with circular groove joining structures is higher than those of other types of joining structure, the radius of circular groove and screw length connecting the fixture and test machine are also affect whole rigidity. The reasonable magnitude of circular groove radius is about (0.17-0.25) times of the board thickness, and screw length is about (1.43-1.55) times of screw nominal diameter, furthermore, the reasonable magnitude of screw pitch determined by self-locking performance and wear resistance of screw pairs.
引文
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