Microstructure-sensitive extreme value probabilities for high cycle fatigue of Ni-base superalloy IN100

To quantify the effects of interactions between various microstructure attributes on fatigue life in the high cycle fatigue (HCF) regime, we have proposed a new microstructure-sensitive extreme value statistical framework. This framework couples the extreme value distributions of certain fatigue indicator parameters (FIPs) or response functions to the correlated microstructure attributes that exist at the extreme value locations of these FIPs. We demonstrate the application of this statistical framework to investigate the microstructure-sensitive fatigue response of the PM Ni-base superalloy IN100 at 650 °C. To accomplish this task, we construct statistical volume elements (SVEs) used to compute the local response for 200 instantiations of IN100. These SVEs are constructed and simulated via the finite element method with crystal plasticity constitutive relations. The results of the simulations are used to explore extreme value statistics of the FIPs for these microstructures. The extreme value distributions of the Fatemi–Socie FIP are fit with high confidence by the Gumbel distribution and are defined in a representative nature with as few as 25 simulated microstructure instantiations (i.e., SVEs). The extreme value marked correlation functions of the apparent Schmid factor based on the geometry of the slip systems relative to the loading direction indicate that cube slip may be important to fatigue crack formation in this material system. This supports previous experimental observations of fatigue crack formation and microstructurally small fatigue crack growth along cube planes in IN100 in grains that are unfavorably oriented for octahedral slip at elevated temperatures.     

增材制造微结构演化及疲劳分散性计算

为了预测增材制造中工艺参数?微结构?力学性能之间的关联规律, 提出了集成离散元、相场模拟、晶体塑性有限元和极值概率理论的计算方法, 揭示了激光扫描速度对微结构演化、屈服应力和疲劳分散性的影响. 首先, 采用离散元实现了重力作用下粉床在已凝固层表面上的逐层铺设; 其次, 通过热?熔体?微结构耦合的非等温相场模拟, 获得了熔体、气孔、晶界、晶粒取向等的时空演化以及最终形成的多晶微结构; 然后, 应用晶体塑性有限元计算了增材制造多晶微结构的宏观力学响应, 并得到表征疲劳裂纹萌生驱动力的疲劳指示参数(FIP); 最后, 采用极值概率理论分析了增材制造多晶微结构的FIP极值分布规律及疲劳分散性. 以316L不锈钢选区激光熔化增材制造为例的计算结果表明: 增材制造微结构的宏观屈服强度随激光扫描速度的增加而降低, 且呈各向异性; FIP极值符合Gumbel极值分布规律, 激光扫描速度增加可降低增材制造微结构疲劳分散性, 但会导致FIP极值升高, 使得疲劳裂纹萌生驱动力增加, 疲劳寿命降低.      

双相钛合金Ti‑6Al‑4V微观缺陷疲劳演化的片层结构分布效应

本文研究疲劳载荷作用下双相钛合金Ti-6Al-4V中片层结构对微观几何缺陷区域演化的影响．基于晶体塑 性有限元(Crystal Plasticity Finite Element, CPFE)理论,建立含微观椭圆缺陷的双相片层代表性体积单元 (Representative Volume Element, RVE)模型,通过调控缺陷附近的微观组织形貌,使缺陷两端分别出现单相结构和 片层结构,以突出双态合金中片层结构分布对微观缺陷演化的影响．模拟结果表明,位于微观缺陷两侧的晶粒, 片层结构的应变敏感性更大,应变沿缺口环向和沿晶内均呈不连贯波动．片层结构通过调节晶内应变,扩大承载 范围,可提高双相钛合金的抗疲劳特性．这一研究结果可为双相钛合金的疲劳裂纹萌生提供一个新的解释途径     

Plasticity in polycrystalline fretting fatigue contacts

Plastic deformation at the scale of microstructure plays an important role in fretting fatigue failure of metals under cyclic loading. In this study, crystal viscoplasticity theory with a planar triple slip idealization is employed to represent crystallographic plasticity in two-dimensional fretting analyses of Ti-6Al-4V. Subsurface deformation maps, fretting maps, and shakedown maps are constructed based on application of J₂ plasticity theory for the polycrystalline substrate. Comparisons are then made with polycrystal viscoplasticity simulations, the latter suggesting that plastic ratchetting plays a significant role in the fretting fatigue process.     

Fatigue crack growth discrepancies with stress ratio

This paper examines cracking in D6ac and 4340 steel along with Mil Annealed and STOA Ti-6Al-4V and finds that the data implies that in the Paris Region (Region II) of the crack growth curve there is only a minimal R ratio dependency. Presented is a theoretical basis for explaining this behaviour and suggest alternative ways for characterising crack growth prediction through the use of the Generalised Frost-Dugdale crack growth law. The Fatigue Damage Map method is then used to explain the physics behind this behaviour.     

A micromechanical basis for partitioning the evolution of grain bridging in brittle materials

A micromechanical model is developed for grain bridging in monolithic ceramics. Specifically, bridge formation of a single, non-equiaxed grain spanning adjacent grains is addressed. A cohesive zone framework enables crack initiation and propagation along grain boundaries. The evolution of the bridge is investigated through a variance in both grain angle and aspect ratio. We propose that the bridging process can be partitioned into five distinct regimes of resistance: propagate, kink, arrest, stall, and bridge. Although crack propagation and kinking are well understood, crack arrest and subsequent “stall” have been largely overlooked. Resistance during the stall regime exposes large volumes of microstructure to stresses well in excess of the grain boundary strength. Bridging can occur through continued propagation or reinitiation ahead of the stalled crack tip. The driving force required to reinitiate is substantially greater than the driving force required to kink. In addition, the critical driving force to reinitiate is sensitive to grain aspect ratio but relatively insensitive to grain angle. The marked increase in crack resistance occurs prior to bridge formation and provides an interpretation for the rapidly rising resistance curves which govern the strength of many brittle materials at realistically small flaw sizes.     

An energy-based microstructure model to account for fatigue scatter in polycrystals

Scatter observed in the fatigue response of a nickel-based superalloy, U720, is linked to the variability in the microstructure. Our approach is to model the energy of a persistent slip band (PSB) structure and use its stability with respect to dislocation motion as our failure criterion for fatigue crack initiation. The components that contribute to the energy of the PSB are identified, namely, the stress field resulting from the applied external forces, dislocation pile-ups, and work-hardening of the material is calculated at the continuum scale. Further, energies for dislocations creating slip in the matrix/precipitates, interacting with the GBs, and nucleating/agglomerating within the PSB are computed via molecular dynamics simulations. Through this methodology, fatigue life is predicted based on the energy of the PSB, which inherently accounts for the microstructure of the material. The present approach circumvents the introduction of uncertainty principles in material properties. It builds a framework based on mechanics of microstructure, and from this framework, we construct simulated microstructures based on the measured distributions of grain size, orientation, neighbor information, and grain boundary character, which allows us to calculate fatigue scatter using a deterministic approach. The uniqueness of the approach is that it avoids the large number of parameters prevalent in previous fatigue models. The predicted lives are in excellent agreement with the experimental data validating the model capabilities.     

Ti-46Al-2Cr-2Nb和Ti6Al4V合金的干摩擦学性能对比研究

本文以商业Ti-6Al-4V合金为参照,考察了Ti-46Al-2Cr-2Nb(原子比)金属间化合物在不同载荷和速率下的干摩擦学行为,结果表明:Ti-46Al-2Cr-2Nb和Ti6Al4V合金的摩擦系数几乎相同,而Ti-46Al-2Cr-2Nb金属间化合物比Ti-6Al-4V具有更好的抗磨性;Ti-46Al-2Cr-2Nb和Ti6Al4V合金的磨损率均随载荷的增加而增加,Ti-46Al-2Cr-2Nb合金磨损率随滑动速率增加而增加,Ti-6Al-4V合金磨损率却随滑动速率增加呈下降直至稳定的趋势;Ti-46Al-2Cr-2Nb合金的磨损机制主要为疲劳磨损,Ti-6Al-4V合金的磨损机制为塑性变形,犁沟和剥落.     

Fatigue crack growth of cable steel wires in a suspension bridge: Multiscaling and mesoscopic fracture mechanics

Intrinsically, fatigue failure problem is a typical multiscale problem because a fatigue failure process deals with the fatigue crack growth from microscale to macroscale that passes two different scales. Both the microscopic and macroscopic effects in geometry and material property would affect the fatigue behaviors of structural components. Classical continuum mechanics has inability to treat such a multiscale problem since it excludes the scale effect from the beginning by introducing the continuity and homogeneity assumptions which blot out the discontinuity and inhomogeneity of materials at the microscopic scale. The main obstacle here is the link between the microscopic and macroscopic scale. It has to divide a continuous fatigue process into two parts which are analyzed respectively by different approaches. The first is so called as the fatigue crack initiation period and the second as the fatigue crack propagation period. Now the problem can be solved by application of the mesoscopic fracture mechanics theories developed in the recent years which focus on the link between different scales such as nano-, micro- and macro-scale.On the physical background of the problem, a restraining stress zone that can describe the material damaging process from micro to macro is then introduced and a macro/micro dual scale edge crack model is thus established. The expression of the macro/micro dual scale strain energy density factor is obtained which serves as a governing quantity for the fatigue crack growth. A multiscaling formulation for the fatigue crack growth is systematically developed. This is a main contribution to the fundamental theories for fatigue problem in this work. There prevail three basic parameters μ^∗, σ^∗ and d^∗ in the proposed approach. They can take both the microscopic and macroscopic factors in geometry and material property into account. Note that μ^∗, σ^∗ and d^∗ stand respectively for the ratio of microscopic to macroscopic shear modulus, the ratio of restraining stress to applied stress and the ratio of microvoid size ahead of crack tip to the characteristic length of material microstructure.To illustrate the proposed multiscale approach, Hangzhou Jiangdong Bridge is selected to perform the numerical computations. The bridge locates at Hangzhou, the capital of Zhejiang Province of China. It is a self-anchored suspension bridge on the Qiantang River. The cables are made of 109 parallel steel wires in the diameter of 7 mm. Cable forces are calculated by finite element method in the service period with and without traffic load. Two parameters α and β are introduced to account for the additional tightening and loosening effects of cables in two different ways. The fatigue crack growth rate coefficient C₀ is determined from the fatigue experimental result. It can be concluded from numerical results that the size of initial microscopic defects is a dominant factor for the fatigue life of steel wires. In general, the tightening effect of cables would decrease the fatigue life while the loosening effect would impede the fatigue crack growth. However, the result can be reversed in some particular conditions. Moreover, the different evolution modes of three basic parameters μ^∗, σ^∗ and d^∗ actually have the different influences on the fatigue crack growth behavior of steel wires. Finally the methodology developed in this work can apply to all cracking-induced failure problems of polycrystal materials, not only fatigue, but also creep rupture and cracking under both static and dynamic load and so on.     

Intergranular strain evolution near fatigue crack tips in polycrystalline metals

The deformation field near a steady fatigue crack includes a plastic zone in front of the crack tip and a plastic wake behind it, and the magnitude, distribution, and history of the residual strain along the crack path depend on the stress multiaxiality, material properties, and history of stress intensity factor and crack growth rate. An in situ, full-field, non-destructive measurement of lattice strain (which relies on the intergranular interactions of the inhomogeneous deformation fields in neighboring grains) by neutron diffraction techniques has been performed for the fatigue test of a Ni-based superalloy compact tension specimen. These microscopic grain level measurements provided unprecedented information on the fatigue growth mechanisms. A two-scale model is developed to predict the lattice strain evolution near fatigue crack tips in polycrystalline materials. An irreversible, hysteretic cohesive interface model is adopted to simulate a steady fatigue crack, which allows us to generate the stress/strain distribution and history near the fatigue crack tip. The continuum deformation history is used as inputs for the micromechanical analysis of lattice strain evolution using the slip-based crystal plasticity model, thus making a mechanistic connection between macro- and micro-strains. Predictions from perfect grain-boundary simulations exhibit the same lattice strain distributions as in neutron diffraction measurements, except for discrepancies near the crack tip within about one-tenth of the plastic zone size. By considering the intergranular damage, which leads to vanishing intergranular strains as damage proceeds, we find a significantly improved agreement between predicted and measured lattice strains inside the fatigue process zone. Consequently, the intergranular damage near fatigue crack tip is concluded to be responsible for fatigue crack growth.     

航空发动机钛合金材料的高周和超高周疲劳性能研究1）

通过对航空发动机空心风扇叶片用Ti-6Al-4V 随炉试样的高周和超高周疲劳试验研究,揭示了Ti-6Al-4V 材料在10⁷ 循环周次以上同样会发生疲劳破坏. 采用三参数幂函数寿命曲线拟合了高周和超高周的疲劳性能数据,发现可以较好地将两种试验下的数据衔接起来,结果显示在此试验条件下基于超声的超高周疲劳试验的频率效应可以忽略. 通过断口分析表明,超高周试样在试样表面没有缺陷的情况下,裂纹大多数是从材料内部或次表面萌生,而高周疲劳试样的裂纹是从材料表面开始萌生.     

The influence of tempering martensite containing microstructures on the near threshold fatigue crack propagation behaviour

Fatigue crack growth studies have been conducted in a humid air environment for various martensite containing microstructures under low and high R-ratio testing conditions.Tempering reduced the yield strength properties; the greater the amount of martensite the greater the reduction.Tempering generally (i) increased the threshold for fatigue crack growth ΔK_th, and (ii) decreased near threshold fatigue crack growth rates for both low and high R-ratio testing conditions. Also tempering inhibited the occurrence of subcritical transgranular cleavage in the high R-ratio tests of the ferrite-martensite microstructures and consequently affected Stage II fatigue crack growth behaviour.Finally the fully martensitic microstructure did not exhibit cracking and the present ΔK_th data exhibited good agreement with other data for steels in the tempered condition.     

快速凝固过共晶铝硅合金的微观组织特征及耐磨性研究

利用单辊旋淬快速凝固法制备Al-21Si和Al-30Si过共晶铝硅合金,采用扫描电镜、透射电镜及XRD技术对所制备合金的组织形貌和相结构进行表征.结果表明:快速凝固合金形成微纳米晶组织,晶粒明显细化.Al-21Si过共晶合金凝固组织由羽毛针状(α-Al+β-Si)共晶体和雪花状α-Al相组成;快速凝固有效抑制初生硅相的形核与生长,α-Al相领先共晶形核生长,形成微纳米级亚共晶组织.Al-30Si高硅过共晶合金初生硅相细小钝化,初晶Si相显微结构为孪晶形貌,呈典型的过共晶组织特征.快速凝固显著提高了合金的显微度和耐磨性,快速凝固Al-21Si合金的耐磨性是传统铸造合金的5倍.     

A reexamination of plasticity-induced crack closure in fatigue crack propagation

The crack closure concept is often used to consider the R-ratio and overload effects on fatigue crack growth. The presumption is that when the crack is closed, the external load produces negligible fatigue damage in the cracked component. The current investigation provides a reassessment of the frequently used concept with an emphasis on the plasticity-induced crack closure. A center cracked specimen made of 1070 steel was investigated. The specimen was subjected to plane-stress mode I loading. An elastic–plastic stress analysis was conducted for the cracked specimens using the finite element method. By applying the commonly used one-node-per-cycle debonding scheme for the crack closure simulations, it was shown that the predicted crack opening load did not stabilize when the extended crack was less than four times of the plastic zone size. The predicted opening load was strongly influenced by the plasticity model used. When the elastic–perfectly plastic (EPP) stress–strain relationship was used together with the kinematic hardening plasticity theory, the predicted crack opening load was found to be critically dependent on the element size of the finite element mesh model. For R = 0, the predicted crack opening load was greatly reduced when the finite element size became very fine. The kinematic hardening rule with the bilinear (BL) stress–strain relationship predicted crack closure with less dependence on the element size. When a recently developed cyclic plasticity model was used, the element size effect on the predicted crack opening level was insignificant. While crack closure may occur, it was demonstrated that cyclic plasticity persisted in the material near the crack tip. The cyclic plasticity was reduced but not negligible when the crack was closed. The traditional approaches may have overestimated the effect of crack closure in fatigue crack growth predictions.     

Analytical and experimental evaluations of the influence of fracture surface roughness,its sliding actions and the associated plasticity on fatigue crack propagation

An investigation of fatigue crack propagation in rectangular AM60B magnesium alloy plates containing an inclined through crack is presented in this paper. The behavior of fatigue crack growth in the alloy is influenced by the fracture surface roughness. Therefore, in the present investigation, a new model is developed for estimating the magnitude of the frictional stress intensity factor, k_f, arising from the mismatch of fracture surface roughness during in-plane shear. Based on the concept of k_f, the rate of fatigue crack propagation, db/dN, is postulated to be a function of the effective stress intensity factor range, Δk_eff. Subsequently, the proposed model is applied to predict crack growth due to fatigue loads. Experiments for verifying the theoretical predictions were also conducted. The results obtained are compared with those predicted using other employed mixed mode fracture criteria and the experimental data.     

Dwell fatigue crack nucleation model based on crystal plasticity finite element simulations of polycrystalline titanium alloys

In this paper a crystal plasticity-based crack nucleation model is developed for polycrystalline microstructures undergoing cyclic dwell loading. The fatigue crack nucleation model is developed for dual-phase titanium alloys admitting room temperature creep phenomenon. It is a non-local model that accounts for the cumulative effect of slip on multiple slip systems, and involves evolving mixed-mode stresses in the grain along with dislocation pileups in contiguous grains. Rate dependent, highly anisotropic behavior causes significant localized stress concentration that increases with loading cycles. The crystal plasticity finite element (CPFE) model uses rate and size-dependent anisotropic elasto-crystal plasticity constitutive model to account for these effects. Stress rise in the hard grain is a consequence of time-dependent load shedding in adjacent soft grains, and is the main cause of crack nucleation in the polycrystalline titanium microstructure. CPFE simulation results are post-processed to provide inputs to the crack nucleation model. The nucleation model is calibrated and satisfactorily validated using data available from acoustic microscopy experiments for monitoring crack evolution in dwell fatigue experiments.     

Hydraulic fracture in poro-hydro-elastic media

The prediction of fluid-driven crack propagation in deforming porous media has achieved increasing interest in recent years, in particular with regard to the modeling of hydraulic fracturing, the so-called “fracking”. Here, the challenge is to link at least three modeling ingredients for (i) the behavior of the solid skeleton and fluid bulk phases and their interaction, (ii) the crack propagation on not a priori known paths and (iii) the extra fluid flow within developing cracks. To this end, a macroscopic framework is proposed for a continuum phase field modeling of fracture in porous media that provides a rigorous approach to a diffusive crack modeling based on the introduction of a regularized crack surface. The approach overcomes difficulties associated with the computational realization of sharp crack discontinuities, in particular when it comes to complex crack topologies including branching. It shows that the quasi-static problem of elastically deforming, fluid-saturated porous media at fracture is related to a minimization principle for the evolution problem. The existence of this minimization principle for the coupled problem is advantageous with regard to a new unconstrained stable finite element design, while previous space discretizations of the saddle point principles are constrained by the LBB condition. This proposed formulation includes a generalization of crack driving forces from energetic definitions towards threshold-based criteria in terms of the effective stress related to the solid skeleton of a fluid-saturated porous medium. Furthermore, a Poiseuille-type constitutive continuum modeling of the extra fluid flow in developed cracks is suggested based on a deformation-dependent permeability, that is scaled by a characteristic length.     

Fatigue damage evolution in silicon films for micromechanical applications

In this paper we examine the conditions for surface topography evolution and crack growth/fracture during the cyclic actuation of polysilicon microelectromechanical systems (MEMS) structures. The surface topography evolution that occurs during cyclic fatigue is shown to be stressassisted and may be predicted by linear perturbation analyses. The conditions for crack growth (due to pre-existing or nucleated cracks) are also examined within the framework of linear elastic fracture mechanics. Within this framework, we consider pre-existing cracks in the topical SiO₂ layer that forms on the Si substrate in the absence of passivation. The thickening of the SiO₂ that is normally observed during cyclic actuation of Si MEMS structures is shown to increase the possibility of stable crack growth by stress corrosion cracking prior to the onset of unstable crack growth in the SiO₂ and Si layers. Finally, the implications of the results are discussed for the prediction of fatigue damage in silicon MEMS structures.     

A non-singular continuum theory of dislocations

We develop a non-singular, self-consistent framework for computing the stress field and the total elastic energy of a general dislocation microstructure. The expressions are self-consistent in that the driving force defined as the negative derivative of the total energy with respect to the dislocation position, is equal to the force produced by stress, through the Peach-Koehler formula. The singularity intrinsic to the classical continuum theory is removed here by spreading the Burgers vector isotropically about every point on the dislocation line using a spreading function characterized by a single parameter a, the spreading radius. A particular form of the spreading function chosen here leads to simple analytic formulations for stress produced by straight dislocation segments, segment self and interaction energies, and forces on the segments. For any value a>0, the total energy and the stress remain finite everywhere, including on the dislocation lines themselves. Furthermore, the well-known singular expressions are recovered for a=0. The value of the spreading radius a can be selected for numerical convenience, to reduce the stiffness of the dislocation equations of motion. Alternatively, a can be chosen to match the atomistic and continuum energies of dislocation configurations.     

A phase field model of electromechanical fracture

Structural reliability analyses of piezoelectric solids need the modeling of failure under coupled electromechanical actions. However, the numerical simulation of failure due to fracture based on sharp crack discontinuities may suffer in situations with complex crack topologies. This can be overcome by a diffusive crack modeling based on the introduction of a crack phase field. In this work, we develop a framework of diffusive fracture in piezoelectric solids. We start our investigation with the definition of a crack surface functional of the phase field that Γ-converges for vanishing length-scale parameter to a sharp crack topology. This functional provides the basis for the definition of suitable dissipation functions which govern the evolution of the crack phase field. Based on experimental results available in the literature, we suggest a non-associative dissipative framework where the fracture phase field is driven by the mechanical part of the coupled electromechanical driving force. This accounts for a hierarchical view that considers (i) the decrease of stiffness due to mechanical rupture as the primary action that is followed by (ii) the decrease of electric permittivity due to the generated free space. The proposed definition of mechanical and electrical parts of the fracture driving force follows in a natural format from a kinematic assumption, that decomposes the total strains and the total electric field into energy-enthalpy-producing parts and fracture parts, respectively. Such an approach allows the insertion of well-known anisotropic piezoelectric storage functions without change. We end up with a three-field-problem that couples the displacement with the electric potential and the fracture phase field. The latter is governed by a micro-balance equation, which appears in a very transparent form in terms of a history field containing a maximum fracture source obtained in the time history of the electromechanical process. This representation allows the construction of a very robust algorithmic treatment based on a operator split scheme, which successively updates in a typical time step the history field, the crack phase field and finally the two piezoelectric fields. The proposed model is considered to be the canonically simple scheme for the simulation of diffusive electromechanical crack propagation in solids. We demonstrate its modeling capacity by means of representative numerical examples.