The Influence of Dwell Time on Low Cycle Fatigue Behavior of Ni-base Superalloy IC10

Anqiang Wang; Lu Liu; Zhixun Wen; Zhenwei Li; Zhufeng Yue

doi:10.1515/htmp-2016-0019

Open Access Published by De Gruyter September 29, 2016

The Influence of Dwell Time on Low Cycle Fatigue Behavior of Ni-base Superalloy IC10

Anqiang Wang , Lu Liu , Zhixun Wen , Zhenwei Li and Zhufeng Yue

From the journal High Temperature Materials and Processes

https://doi.org/10.1515/htmp-2016-0019

Abstract

Low cycle fatigue and creep-fatigue experiments of IC10 Ni-base superalloy plate specimens with multiple holes were performed below 1,000 °C. The average fatigue life is 10^5.4 cycles, while the creep-fatigue life is 10^3.4 cycles, which shows that the life of creep-fatigue is reduced 1–2 times compared with low cycle fatigue life. After tests, the detailed fracture and microscopic structure evolution were observed by scanning electron microscopy (SEM); meanwhile, the constitutive model based on crystal plasticity theory was established and the fracture mechanism was analyzed. Three conclusions have been obtained: First, the load during dwell time leads to the damage accumulation caused by deformation and the interaction of fatigue and creep shortens the service life of materials seriously. Second, in order to maintain the macroscopic deformation, a new slip plane starts to makes the dislocation slide in reverse direction, which leads to fatigue damage and initial cracks. Third, the inner free surface creates opportunities for escape of the dislocation line, which is caused by the cavity. What’s more, the cure dislocation generated by cyclic loading contributes to the formation and growth of cavities.

Keywords: low cycle fatigue; crystal plasticity; microstructure

Introduction

IC10 Ni-base superalloy is widely used in critical components of gas turbine for its excellent creep and fatigue performance at high temperature. However, the existence of casting defects and film cooling holes, resulting in stress concentration and microcracks, seriously affect the mechanical performance. To make full use of properties of the material and ensure no destructive accidents occurring during the design life, an accurate mechanical model to simulate the working condition of single crystal blade is badly needed. Turbine components always experience rather complex loading history with the action of high temperature and alternating stress. Low cycle fatigue and creep are the main fracture mechanisms in many fracture modes [1, 2]. As for the mechanical response of Ni-base superalloy under the above two loading conditions, considerable researches have been carried out theoretically and experimentally at home and abroad [3, 4, 5]. Certain progress has been made and the corresponding elastic-plastic, creep and fatigue model have been put forward. Relatively, the mechanical response analysis model of Ni-base single crystal under the interaction of fatigue and creep is far more less [6]. In different working stages, the blade bears the fatigue damage and creep damage separately caused by periodic change of centrifugal force and average stress. Hence the mechanical response under the interaction of fatigue and creep must be considered during application and design of single crystal blades.

Low cycle fatigue and creep-fatigue experiments on thin-plate specimens with more exhaust film cooling holes were carried out. The finite element model was built based on SEM analysis, the fracture and microscopic damage mechanism of the simulated specimens was analyzed. A damage model based on continuum damage mechanics has been put forward in this paper, which assess the life of nickel base single crystal alloy through the analysis by one or a limited number of representative cycles [7]. This work hopes to provide reference for the mechanic research and design and the life prediction of film cooling blades.

Experiments

Material description

IC10 alloy is a Ni₃Al-based directionally solidified alloy along [001] direction. It is a typical LI₂ type multiphase material and its chemical composition is shown in Table 1. The directionally solidified alloy is a kind of transitional material between isometric and single crystal. The phase distribution of its grain from transverse view is random. Generally, the directionally solidified alloy can be seen as the approximate transverse isotropic material when its grain number is enough. Focused on the mechanical properties of IC10 along [001] direction in this paper, Zhang [8] put it forward that only octahedral slip system move along the sliding motion regardless of the temperature. All the specimens are plate-castings with 14 film cooling holes whose diameter is 0.5 mm. The detailed size of the specimen is shown in Figure 1. The experimental temperature is 1,000 °C, stress ratio is 0.1, the maximum stress is 200 MPa, the loading frequency of fatigue experiments is 3 hz and the dwell time of the creep-fatigue experiments is 15 s. The loading waveform is shown in Figure 2.

Table 1:

Chemical composition of IC10 alloy/w%.

C	Co	Cr	Al	W
0.07～0.12	11.5～12.5	6.5～7.5	5.6～6.2	4.8～5.2
Mo	Ta	Hf	B	Ni
1.0～2.0	6.5～7.5	1.3～1.7	0.01～0.2	0.07～0.12

Figure 1:

Geometry size of specimen.

Figure 2:

Loading curve. (a) Low-cycle fatigue; (b) Fatigue with dwell time.

Experiment results

The life of creep-fatigue is reduced 1–2 times compared with the low cycle fatigue life. The average deformation of fatigue specimen is about 1 mm and cyclic creep specimen is more than 4 mm at final fracture. The plastic deformation of creep-fatigue specimen is about four times than that of fatigue specimen and the fracture mechanism of the above two groups of specimen shows obvious difference. In order to describe the plastic deformation accurately, the deformation of several typical cycles was selected and shown in Figure 3: the plastic deformation of creep-fatigue specimen at 10th cycle increased by 130 percent than fatigue specimen.

Figure 3:

Plastic deformation curve of typical cycle.

Fracture analysis

Macroscope fractography

Based on the linear elastic theory, the maximum stress exists at the edge of the holes and is perpendicular to the tensile axis, where early strain concentrates [9]. In all experiments, cracks appear first at the edge of the holes then extend to the direction which is normal to maximum stress. As is shown in Figure 4(a), the main origin surface of fatigue crack is perpendicular to the tensile direction. At the beginning, the fracture is vertical to primary stress, with the crack expansion, the fracture forms a 45 degree angle with principal stress, which is a typical kind of fatigue fracture morphology [10]. As is shown in Figure 4(b), area reduction and the deformation of creep-fatigue specimens are much more serious, and more cracks were observed on the edge of holes. Apart from the reduction of effective bearing area, these round center holes tend to be elliptical ones, belonging to multi-source craze. The interference effect and slip band stripes are obvious among holes, and larger plastic deformation occurs during dwell time. All these factors lead to the accumulation of fatigue damage and shorten the service life of materials.

Figure 4:

Growth path of crack. (a) Fatigue with dwell time; (b) Low-cycle fatigue.

Microstructure analysis

The microstructure of fatigue is shown in Figure 5(a). It is flat on the left side of holes, however, the microstructure of fatigue on the right side and between two holes is relatively coarse. We may infer that the plate specimen began to crack from the left side of the hole and was snapped instantly when the crack extended to the right margin, which is typical fatigue fracture. The morphology of fatigue propagation region is shown in Figure 5(b). Ridge strip shells are clearly visible around the hole.

Figure 5:

Microstructure of low-cycle fatigue specimen.

The fracture morphology of creep-fatigue and fatigue is different along [001] direction. As is shown in Figure 6(a), cracks initiate from the center hole. Crack sources and cleavage morphology are distributed around the holes and obvious dimples, voids and oxidation zone are observed. The micro-voids scattering around film holes are potential crack initiation area, of which the microstructure morphology is shown in Figure 6(b). The left and right edge of specimens are final fatigue rupture region and the section consisting of multiple sliding surface crystallographic plane is neat and smooth, which is similar with the creep fracture [10].

Figure 6:

Microstructure of creep-fatigue specimen.

The microstructure of typical sections of two group specimen after polishing and corroding is as follows. The original as-cast of IC10 alloy is irregular cubic matrix, which consists of γ, γ′ and γ+γ′ eutectic phase [11]. After the cyclic creep test, the γ′ phase changes from as-cast irregular cubic to globular because the effect of high temperature and high stress, and the microstructure is shown in Figure 7(a). Compared with the morphology of creep, the change of γ′ phase is not obvious, although the γ′ phase has changed from cubic to globular, as is shown in Figure 7(b).

Figure 7:

Morphology of γ′ phase. (a) Dwell 15 s; (b) Without dwell time.

The microstructure evolution of longitudinal section is shown in Figure 8(a) and (b). The heat affected zone and recast layer weakened the performance of the material [12]. Meanwhile, the complicated structure caused stress concentration and greater interference effect during experiment, the change of γ′ phase near the hole is more obvious than these far-away ones, large numbers of γ′ phase have grown up obviously.

Figure 8:

Morphology of γ′ phase near the hole. (a) Dwell 15 s;(b) without dwell time.

Finite element analysis (FEA)

Constitutive model

Almost all experiments show that the movement of slip system is the main mechanism of single crystal deformation. The rate-dependent crystal plasticity is adopted to describe the deformation behavior of Ni-base crystal in this paper. Based on the sliding deformation mechanism, shear strain is used to describe slip. The shear strain rate on a slip system correlates with the shear stress, which is defined as follows.

(1)τα=Pα:σ

where τα is shear stress, σ is stress tensor, Pα is orientation parameter, defined as:

(2)Pα=12mαnαT+nαmαT

where nα and mα are the unit vectors normal to the slip plane and along the slip direction of slip system σ respectively.

Considering the plastic deformation of cyclic loading condition, we add back stress to the visco-plastic relation suggested by Hutchinson, which is used to describe the rule of slip system resolve shear strain of single crystal material. A power law relation is adopted to describe the relation of the resolved shear strain rate γ˙α and the resolved shear stress τα as follows:

(3)γ˙α=γ˙0ατα−Xg0α1msgnτα−X

where g0α is the reference shear stress, γ˙0α is the reference resolved shear strain rate, m is the strain rate sensitivity exponent, sgn() was the sign function, which is defined as sgn()=−1 if x <0 andsgnx=1 if x ≥ 0.

The back stress X is described by the kinematic hardening rules and the evolutionary equation of X is expressed as follows:

(4)X˙=Caγ˙α−X−Yγ˙α−dexp−QRTXnsgn X

(5)Y˙=−αYstsgnX+YXn

where C,a,d,Q,R,α are the material constants, T is temperature, the variableY expressed the dynamic recovery term of the back stress, Yst denotes the saturation value of Y, the third term on the right-hard side in eq. (4) expressed the thermal recovery term of the back stress.

The material strain hardening could be specified by the evolution of the function, which g0α is modeled by the following equation:

(6)g˙0α=∑β=1Nhαβγ˙β

where hαβ is the hardening coefficient, which could be obtained as:

(7)hαβ=qαβhβ

qαβ is the matrix describing the latent hardening, and hβ is a single hardening rate. Here it is expressed as follow:

(8)hβ=h01−τατsa

where h0 is hardening modulus， τs and a are model parameters.

The above rate-dependent constitutive equation has been implemented into the commercial finite element software ABAQUS through user subroutine (UMAT) and simulate the deformation mechanism of fatigue and creep-fatigue behavior. The parameters of constitutive model and kinematic hardening rule are shown in Tables 2 and 3. The fatigue hardening of stress–strain relationship is shown in Figure 9 The single crystal material presents obvious ratcheting effect under asymmetrical loading condition. With the accumulation of ratcheting strain, the performance of material is weakened continually and will crack after a certain number of loops.

Table 2:

Material parameters of crystallographic constitutive.

T/°C	E(MPa)	ν	G(MPa)	γ˙0(α)	m	a	g0(α)	h₀	*τ_s*
1,000	86,700	0.463	101,500	0.031	0.12	1.3	125	368.4	359

Table 3:

Material constants of kinematic rule.

C	a	d	Q	R	α	m	*Yst*
6.0	150.0	4.5×10⁻⁷	85.0	8.31	1.6×10⁻⁷	4.275	5.0

Figure 9:

Ratcheting effect of low-cycle fatigue.

Previous studies have shown that fatigue damage plays a main role in the cyclic creep experiment of plate specimen with film holes. Meanwhile, the dwell time has an important effect on the service life of the specimen [13]. Stress–strain relationship of creep-fatigue is obtained by simulation, as shown in Figure 10. The deformation of creep-fatigue experiment during the dwell time is obvious. In the initial cycles, plastic deformation is larger and gradually reaches a steady state with the increase of loops. The linear distance between loading section and unloading section in the stress–strain relationship curve reflects the hardening behavior of the materials. The fatigue performance of material was improved with the reduction of plastic deformation.

Figure 10:

Ratcheting effect of fatigue with dwell time.

Damage model

Cyclic damage mechanism

From the micro perspective, the movement of dislocation on the slip plane results in the plastic deformation. As for ideal material, any dislocation toward a certain direction will move backward without any damage under the action of reverse stress. However, for real material, dislocation movement under reverse stress happens sometimes, partial dislocation will be tied and can’t move back. In order to maintain themacroscopic deformation, a new slip plane starts to makes the dislocation slide in reverse direction,which leads to fatigue damage and initial cracks.

This kind of damage belongs to fatigue damage, irrelevant with the load time, completely depending on the reverse number of load and the cyclic response. The following model can be used to determine the accumulation of fatigue damage: when the slip plane τeffα is greater than critical resolved shear stress τcrssα, the dislocation will move reversely and cause damage. The overall damage for the material is calculated as follows:

(9)ΔDi fat=∑α=1nΔDfatα

For Ni-base single crystal superalloy, the critical plane is usually the crystal slip plane. Arakere [14, 15] has proven that fatigue life of Ni-base single crystal material is closely related to the maximum resolved shear stress among all slip systems. Apparently, slip and dislocation densities will increase with the increase of resolved shear stress. Assuming that the reverse loading keeps the rate of pinned dislocations stable, the number of pinned dislocation would increase, which restrains the reverse movement of the dislocation severely. The increase of the stress leads to the increase of damage in every single cycle. So the resolved shear stress and slip rate are suitable to quantify the fatigue damage.

Tinga [16] suggested a cycling damage model based on these factors. The evolution of the cycle damage is as follows.

(10)ΔDi fat=∑α=112τmaxαSfoctmfoctγ˙maxαγ˙foctnfoct

τmaxα is the maximum resolved shear stress and γ˙maxα is the maximum shear strain rate. The reference stress Sfoct is defined as the scale factor, 4.25 times of the critical resolved shear stress. Parameters γ˙foct，mfoct，nfoct are determined by experiment results, which are shown in Table 4.

Table 4:

Parameters of life model.

*m_foct*	*n_foct*	γ˙foct	*s_foct*	*m_croct*	*n_croct*	γ˙croct	*s_croct*
9.5	0.3	10	531	4.936	0.04	10⁻⁶	3,100

We can find that the maximum stress and damage first appears near the film cooling hole and results in the fracture of specimen (through calculation), which is consistent with the experiment results. The simulated cyclic fatigue damage evolution of structure is shown in Figure 11: with the accumulation of cycles, the damage of each cycle decrease and tends to be stable, so the stable cyclic damage can be used to quantify the fatigue life of material.

Figure 11:

Damage evolution of low-cycle fatigue.

Creep damage mechanism

Different from cyclic damage, creep damage belongs to time-dependent damage. The formation and growth of micro-cavities in the material play a prominent role in damage accumulation under creep condition [17]. Metallographic inspection of creep specimen by Moss et al. [18] revealed that cracks initiated from pre-existing micro-pores originating from the casting process, also new micro-voids were formed at the γ/γ′-interface. Another important mechanism under creep condition is the microstructure coarsening effect known as rafting. The original cuboidal precipitates, combined with certain stress, transform into elongate plates above 850 °C [19, 20]. The change of morphology of matrix phase which bears the majority of the plastic deformation has a great effect on the material mechanical response.

Comparing the two groups of experiment we can see that damage in creep stage accounts for a large proportion in total damage and reduces the cycle number. Many damage models assume two damages are uncorrelated and can be linearly superposition together, mainly based on the classical Palmgren-Miner and Robinson [21] equation. But the test results show that there are obvious effects between the two damage mechanisms.

For the time-dependent creep damage, Levkovitch et al. [22] ported the equation [23] to crystalline plasticity and got the time-dependent damage model of nickel-base single crystal. The evolution of damage D based on the resolved shear stress τα and slip rate γ˙α of all the slip system.

(11)D˙icr=∑α=112D˙crα=∑α=112ταScrcotmcroctγ˙αγ˙croctncroct

Parameters mcroct，ncroct are determined by experiment, which are shown in Table 4.

Creep-fatigue damage model

Creep rupture was caused by the formation and growth of micro-voids while fatigue rupture was produced by the dislocation curing of reverse slip. The interaction of two kinds of damage can be interpreted as that the cavity generated by creep provide inner extra surface, which creates opportunities for dislocation line to escape, therefore the reverse slip is strengthened. On the other hand, the cure dislocation produced by cyclic loading contributes to the generation and growth of cavity. Under this condition, the existence of any kind of damage will affect the other damage accumulation.

In creep-fatigue tests, combining fatigue and creep damage and also considering the interaction between the two damages, Tinga [16] put forward the following creep-fatigue damage model, the damage mechanism is as follows:

(12)Ditot=Dicr+Di fat+AintDicrDi fatDicr+Di fat

The parameter Aint is the interaction factor. When Aint=3, the damage evolution of creep-fatigue is shown in Figure 12.

Figure 12:

Damage evolution of fatigue with dwell time.

Creep-fatigue life model

The calculation of damage doesn’t affect the cyclic deformation of fatigue behavior. When the damage is equal to 1, calculation end automatically and the cycle number at this moment is the fatigue life under the loading condition. Meanwhile, the cycle deformation will soon reach a steady state and the mean value of maximum tensile stress keeps stable. And in this paper, the tensile damage D1fat in extensional phase of fourth cycle is regarded as the rest of damage. According to the loading time Δt, the damage in the creep stage can be expressed as D1crΔt. Consequently, considering the interaction effect, the life equation of cyclic creep can be expressed as follows:

(13)Nfc=1/(D1crΔt+D1 fatΔt+AintD1cr∗D1 fatD1cr+D1 fat)

According to the above analysis, the fitting method of life parameter will be based on the calculation results of elastic plastic. The life under the interaction of fatigue and creep is determined by fatigue damage, creep damage and the coefficient of interaction. The comparison of calculation and experiment results is shown in Figure 13.

Figure 13:

Contrast of logarithmic life.

Conclusion

The fracture mechanism of fatigue and creep-fatigue has obvious difference. The load during dwell time leads to the damage accumulation caused by the deformation and then reduces the life of single crystal material seriously.
In the process of cyclic loading deformation, partial dislocation will be tied and can’t move back. In order to maintain the macroscopic deformation, a new slip plane starts to makes the dislocation slide in reverse direction, which leads to fatigue damage and initial cracks.
The interaction effect of creep and fatigue is as follows: the inner free surface creates opportunities for escape of the dislocation line, which is caused by the cavity. And the cure dislocation generated by cyclic loading contributes to the formation and growth of cavities.

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Received: 2016-2-21

Accepted: 2016-6-15

Published Online: 2016-9-29

Published in Print: 2017-9-26

This article is distributed under the terms of the Creative Commons Attribution Non-Commercial License, which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.

The Influence of Dwell Time on Low Cycle Fatigue Behavior of Ni-base Superalloy IC10

Abstract

Introduction

Experiments

Material description

Experiment results

Fracture analysis

Macroscope fractography

Microstructure analysis

Finite element analysis (FEA)

Constitutive model

Damage model

Cyclic damage mechanism

Creep damage mechanism

Creep-fatigue damage model

Creep-fatigue life model

Conclusion

References

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