CN110967268A - 一种考虑加载频率效应的粘弹性多轴循环应力应变关系确定方法 - Google Patents

一种考虑加载频率效应的粘弹性多轴循环应力应变关系确定方法 Download PDF

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CN110967268A
CN110967268A CN201911338631.3A CN201911338631A CN110967268A CN 110967268 A CN110967268 A CN 110967268A CN 201911338631 A CN201911338631 A CN 201911338631A CN 110967268 A CN110967268 A CN 110967268A
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尚德广
崔进
常东帅
王灵婉
李道航
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Abstract

本发明公开了一种考虑加载频率效应的粘弹性多轴循环应力应变关系确定方法，这种方法将应变分为弹性应变和粘性应变，弹性应变采用胡克定律进行计算，粘性应变通过引入加载频率作为参数进行计算，将二者运用到复合材料循环本构关系计算方法中。利用T700/MTM28树脂基复合材料圆管结构件在多轴加载下的试验数据进行了验证，发现本方法能够较好地描述树脂基复合材料在多轴加载下的循环应力应变关系。因此，本方法能够提高航空航天、军工设备和其他复合材料产品部件疲劳强度设计的可靠性，具有重大工程意义。

Description

一种考虑加载频率效应的粘弹性多轴循环应力应变关系确定 方法
技术领域
本发明属于多轴机械疲劳强度理论领域，尤其涉及一种多轴机械加载下复合材料应力-应变状态确定方法。
背景技术
在航天航空领域中，复合材料已经被大量用于制作机械结构。在工程服役中的复合材料经常承受复杂的机械载荷特别是动态交变载荷，这些载荷将会使结构不可避免地产生裂纹、过度变形和最终的疲劳失效。系统的研究材料的疲劳性能可以有效防止机械结构发生因疲劳产生的机械事故。为了研究复合材料的疲劳性能，有必要对材料在循环加载下的变形行为，并根据变形行为来建立精确的循环本构模型。循环本构模型也是疲劳寿命预测和有限元仿真的基础。
树脂基复合材料由纤维和树脂基体组成。纤维起着承载作用，基体起着纤维间的粘结作用。一般情况下，室温下的树脂在动态载荷也会表现出粘性，这是树脂基复合材料具有粘性特征的主要原因。粘性意味着材料的力学属性与加载速率有着密切的关系。
发明内容
本发明目的在于针对多轴加载下复合材料疲劳强度设计的需求，提出了一种多轴加载下循环应力-应变确定方法。与现有技术相比，本发明考虑了由于复合材料基体具有粘性特征而产生的加载频率对材料循环应力-应变关系的影响。
本发明的技术方案为一种考虑加载频率效应的粘弹性多轴循环应力应变关系确定方法，本方法实现的步骤如下：
步骤(1)：确定基本参数，读取加载载荷谱，计算名义应力历程；
步骤(2)：根据轴向弹性模量和扭向剪切模量分别计算轴向弹性应变εx_纅和扭向弹性剪切应变εxy_纅：
Figure BDA0002331650220000021
Figure BDA0002331650220000022
上式中，E表示弹性模量，G表示剪切模量，E和G可通过单轴试验循环应力应力幅和单轴循环应变幅获得：
Figure BDA0002331650220000023
Figure BDA0002331650220000024
上式中，Δσx表示轴向应力幅值，Δτxy表示剪切应力幅值。
步骤(3)：计算t到t+Δt时刻的轴向应力增量Δσx和扭向剪切应力增量Δτxy；
步骤(4)：分别计算轴向应力σx和扭向剪切应力τxy在t时刻到t+Δt时刻的变化速率
Figure BDA0002331650220000025
和
Figure BDA0002331650220000026
步骤(5)：分别计算拉伸和扭转载荷下的粘性应变εx_v和εxy_I:
Figure BDA0002331650220000027
Figure BDA0002331650220000028
其中，ξ1和ξ2分别表征材料在轴向和扭向的粘性程度，可分别由轴向单轴拉伸和单轴扭转循环应力应变试验获得：
Figure BDA0002331650220000031
Figure BDA0002331650220000032
步骤(6)：计算轴向应变εx和扭向应变εxy:
Figure BDA0002331650220000033
Figure BDA0002331650220000034
与现有技术比较，本发明提出了一种考虑加载频率效应的粘弹性多轴循环应力应变关系确定方法，这种方法考虑了加载频率影响，并将这种影响进行量化，物理含义明确，计算过程简单。通过对比多轴加载下的循环应力应变试验数据，本发明提出的方法具有很高的精确度，具有重大工程意义。
附图说明
图1加载路径。
图2试件尺寸。
图3本方法实施流程图。
图4多轴加载下本方法预测得到应力应变数据与试验数据对比图。3Hz加载频率和75％的静强度加载，(a)比例加载；(b)相位角：45°；(c)相位角：90°。
具体实施方式
结合附图说明本发明。
采用T700/MTM28树脂基复合材料的圆管结构件的多轴加载下试验数据为本发明作进一步说明，试件尺寸及形状如图1所示，施加到结构件上的加载路径如图2所示。
一种考虑加载频率效应的粘弹性多轴循环应力应变关系确定方法，具体计算方法如下：
步骤(1)：计算名义应力。加载形式分别为沿圆管纵向的拉伸和扭转双轴加载,这两种载荷在圆管截面上引起的名义应力分别为：
Figure BDA0002331650220000041
Figure BDA0002331650220000042
其中，D和d分别为圆管的外径和内径，Fn和M分别为轴向拉伸(压缩)力和扭矩；
步骤(2)：根据轴向弹性模量和扭向剪切模量分别计算轴向弹性应变εx_纅和扭向弹性剪切应变εxy_纅：
Figure BDA0002331650220000043
Figure BDA0002331650220000044
其中，弹性模量E和剪切模量G可通过单轴试验循环应力应力幅和单轴循环应变幅获得：
Figure BDA0002331650220000045
Figure BDA0002331650220000051
步骤(3)：计算t到t+Δt时刻的轴向应力增量Δσx和扭向剪切应力增量Δτxy；
步骤(4)：分别计算轴向应力σx和扭向剪切应力τxy在t时刻到t+Δt时刻的变化速率
Figure BDA0002331650220000052
和
Figure BDA0002331650220000053
步骤(6)：分别计算拉伸和扭转载荷下的粘性应变εx_v和εxy_v:
Figure BDA0002331650220000054
Figure BDA0002331650220000055
其中，ξ1和ξ2分别表征材料轴线和扭向的粘性程度，可分别由轴向单轴拉伸和单轴扭转循环应力应变试验获得：
Figure BDA0002331650220000056
Figure BDA0002331650220000057
步骤(7)：计算轴向应变εx和扭向应变εxy:
Figure BDA0002331650220000058
Figure BDA0002331650220000059
通过重复步骤(2)到步骤(7)，获得多轴加载下的循环应力应变关系。
为了验证本发明提出的多轴加载下树脂基复合材料的应力应变确定方法，将本方法得到的多轴加载的应变历程和对T700/MTM28树脂基复合材料多轴加载试验得到的应变历程进行了对比，对比结果如图3所示。可以发现，由本方法得到的数据和试验数据吻合较好，说明本方法精确的预测了多轴加载下树脂基的应力应变状态。因此，本方法能够提高航空航天、军工设备和其他复合材料结构疲劳强度设计的可靠性，具有重大工程意义。

Claims (2)

1.一种考虑加载频率效应的粘弹性多轴循环应力应变关系确定方法，其特征在于，该方法的实现步骤如下，
步骤(1)：确定基本参数，读取加载载荷谱，计算名义应力历程；
步骤(2)：根据胡克定律分别计算轴向弹性应变εx_e和扭向弹性剪切应变εxy-e：
Figure FDA0002331650210000011
Figure FDA0002331650210000012
步骤(3)：计算t到t+Δt时刻的轴向应力增量Δσx和扭向剪切应力增量Δτxy；
步骤(4)：分别计算轴向应力σx和扭向剪切应力τxy在t时刻到t+Δt时刻的变化速率
Figure FDA0002331650210000013
和
Figure FDA0002331650210000014
步骤(5)：分别计算拉伸和扭转载荷下的粘性应变εx_v和εxy_v:
Figure FDA0002331650210000015
Figure FDA0002331650210000016
其中，ξ1和ξ2分别表征材料在轴向和扭向的粘性程度，分别由轴向单轴拉伸和单轴扭转循环应力应变试验获得：
Figure FDA0002331650210000017
Figure FDA0002331650210000018
步骤(6)：计算轴向应变εx和扭向应变εxy:
Figure FDA0002331650210000021
Figure FDA0002331650210000022
2.根据权利要求1所述的一种考虑加载频率效应的粘弹性多轴循环应力应变关系确定方法，弹性模量E和剪切模量G通过单轴试验循环应力应力幅和单轴循环应变幅获得：
Figure FDA0002331650210000023
Figure FDA0002331650210000024
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