1、疲劳分析简介 2012.10.01 载荷和应力的分类 静应力 ： 不随时间变化或变化缓慢的应力 。 变应力：随时间变化的应力 。 变 应力又可分为 稳定周期变应力 非稳定 周期变应力 随机变应力 最基本的 变应力为稳定周期变应力 力 。 疲劳分析的分类 高周期 疲劳 与 低 周期 疲劳 1 101 102 103 104 105 106 107 108 低 周 期疲 劳 高 周 期疲 劳 永久使用 N rmaxo N0 S-N curve N 疲 劳极限 预测裂缝的 开始 与 成长 低 周 期疲 劳 Introduction Low-cycle fatigue analysis is a qu
2、asi-static analysis of a structure subjected to sub-critical cyclic loading. It can be associated with thermal as well as mechanical loading. In Abaqus can simulate low-cycle fatigue in: bulk ductile materials material interfaces Low-cycle Fatigue in Bulk Materials Abaqus/Standard提供一 个 分析延性 金属 材料，在
3、反复 施力下 累积 非 弹性应变 能而造成的 损伤与 失效的功能 Low-cycle fatigue里 的 损伤定义与 我們平常 定义 的材料 损伤 分析(continuum damage approach)大致相同： a constitutive behavior of undamaged ductile materials; a damage initiation criterion; and a damage evolution response. The damage initiation and evolution are characterized by the stabilize
4、d accumulated inelastic hysteresis strain energy per stabilized cycle. (w) Note: Damage initiation and evolution for low-cycle fatigue analysis is currently not supported in Abaqus/CAE. Low-cycle Fatigue in Bulk Materials Example: Thermal cycling failure of solder joint Solder joint reliability anal
5、ysis of automotive electronics under cyclic thermal loading. The crack propagates forward Low-cycle Fatigue in Bulk Materials Quarter-symmetry model: Solder material (63Sn/37Pb) Modeled using temperature-dependent elasticity and power-law creep. Low-cycle fatigue analysis run for 801 cycles. Each th
6、ermal cycle is 1920 seconds. Define the low-cycle fatigue analysis step *STEP, INC=800 *DIRECT CYCLIC, FATIGUE 60., 1920., 29, 29, 100 50, 100, 801, 1.1 Temperature load in once cycle Quarter-symmetry model electronic chip printed circuit board gullwing leads solder joints Low-cycle Fatigue in Bulk
7、Materials Damage initiation criterion for ductile damage in low-cycle fatigue The onset of damage in low-cycle fatigue is characterized by the accumulated inelastic hysteresis energy per cycle, w, in a material point when the structure response is stabilized in the cycle. The cycle number (N0) in wh
8、ich damage is initiated is given by where c1 and c2 are material constants. Note: c1 depends on the system of units in which you are working; care is required to modify c1 when converting to a different system units. The initiation criterion can be used in conjunction with any ductile material. Dama
9、ge initiation criterion output: CYCLEINI Number of cycles to initialized the damage 201 cN c wLow-cycle Fatigue in Bulk Materials Damage evolution for ductile damage in low-cycle fatigue Once the damage initiation criterion is satisfied at a material point, the damage state is calculated and updated
10、 based on the inelastic hysteresis energy for the stabilized cycle. The rate of the damage (dD/dN) at a material point per cycle is given by where c3 and c4 are material constants, L is the characteristic length associated with the material point, and D is the scalar damage variable. The details of
11、choosing characteristic length will be discussed later. Note: c3 depends on the system of units in which you are working; care is required to modify c3 when converting to a different system units. 43 ccwdDd N LLow-cycle Fatigue in Bulk Materials Results Damage initiation at joint toe Cycle number 19
12、9 Damage evolution Cycle number 749 Damage evolution Cycle number 801 Low-cycle Fatigue at Material Interfaces The onset and fatigue delamination growth at the interfaces are characterized by using the Paris Law, which relates crack growth rates da/dN to the relative fracture energy release rate G,
13、G = Gmax Gmin where Gmax and Gmin correspond to the strain energy release rates when the structure is loaded up to Pmax and Pmin, respectively. The Paris regime is bounded by Gthresh and Gpl. Below Gthresh, there is no fatigue crack initiation or growth. Above Gpl, the fatigue crack will grow at an
14、accelerated rate. a: crack length N: number of cycles G: strain energy release rate Gthresh: strain energy release rate threshold Gpl: strain energy release rate upper limit GequivC: critical equivalent strain energy release rate Low-cycle Fatigue at Material Interfaces fatigue crack initiation The
15、fatigue crack growth initiation criterion is defined as: where c1 and c2 are material constants. The interface elements at the crack tips will not be released unless the above equation is satisfied and Gmax Gthresh. 21 1 .0 ,cNfcGa: crack length N: number of cycles G: strain energy release rate Gthr
16、esh: strain energy release rate threshold Gpl: strain energy release rate upper limit GequivC: critical equivalent strain energy release rate Low-cycle Fatigue at Material Interfaces Fatigue delamination growth Once the delamination growth criterion is satisfied at the interface, the crack growth ra
17、te da/dN can be calculated based on G. da/dN is given by the Paris Law if Gthresh0 r 0 高 应 力 低 寿命 装配后 的最大主 应 力 排 气 管受 热膨胀后 的最大主 应 力 高 应 力 低 寿命 排 气 管 寿 命 排 气 管受 热膨胀后 的最大 機 械零件的疲 勞強 度 計 算 3 不 稳 定 应变 力 时 的 疲劳强度计算 t 規律性不穩定 变应 力 機 械零件的疲 勞強 度 計 算 3 當 损伤 率 达 到 100%时 ，材料即 发 生疲 劳 破 坏 ， 对应于极限状况 有： 1332211 NnN
18、nNn不 稳 定 应变 力 时 的 疲劳强度计算 如何 推测 S-N curve? N max UTS 1 107 r = 0 疲 劳极限(应 力 ) 疲 劳 比 ( Endurance ratio ) 疲 劳 比 就是 疲劳极限对 抗拉 强度 之 比值。 通常 钢 之疲 劳 比 約 0.45 0.55 之間 ,但 对 有 凹痕或被腐蝕 的 试杆 而言 ,其 比值 会 降低。 钢 的 疲劳极限与 抗拉 强度 之 关系图 疲劳 限和 疲劳强度 強 度 之 关系 表 疲劳 分析 软件 FE-safe 为 何 需要疲劳 分析 软件 ? 1. 考虑制造过程 或 组装产生 的 预应力 2. 考虑多种 load case 3. 在一 个周 期 负载 中，最大 应 力的 发生 位置不固定 4. 乱数震动 造成的 疲劳 5. 热疲劳 6. 焊接 疲劳 7. 疲分析簡介 謝謝 !
