text stringlengths 0 1.19M |
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cycles. Stress intensity range at the border of the IAA, ΔKIAA can be calculated using Eq. shows ΔKIAA versus cycles to failure. It may be noticed, that ΔKIAA is almost constant irrespective of cycles to failure. For the present material and loading conditions the stress intensity range is ΔKIAA |
= 4.0 ± 0.2 MPa m1/2. Stress intensity range can also be calculated for a crack with area=areafish-eye. With the measured sizes of the fish-eyes, the stress intensity range at the border of the fish-eyes is ΔKfish-eye |
= 7.4 ± 0.8 MPa m1/2.The depths of the crack-initiating inclusions below the specimen surface are shown in . Seven classes of 25 μm width are shown. No crack-initiating inclusion was found closer than 25 μm to the surface. In a distance between 25 μm and 50 μm to the surface, six crack-initiating inclusions are located... |
cycles and interior inclusion-induced failure above Fatigue cracks are initiated exclusively at TiN nonmetallic inclusions in the present 18Ni maraging steel. The fracture surface enclosing the inclusions appears granular and homogeneous without steps or secondary cracks and it does not indicate the crack propagation d... |
= 4 MPa m1/2 and 6 MPa m1/2Progress of fatigue damage in the investigated steel may be captured assuming a slowly propagating crack. An adapted Paris law is suggested by Tanaka and Akiniwa is used to describe the dependence of stress intensity range ΔK and crack propagation rate Δ(area)/ΔN.Lifetimes are calculated by ... |
= 8.04 and C |
= 1.10 × 10-16.Scatter of data using the parameter ΔKINC may be quantified using the ratio TK of N/(area)1/2 with 90% fracture probability and N/(area)1/2 with 10% fracture probability. Data points are normalised using Eq. , and fracture probability is determined assuming a log-normal distribution. The ratio TK |
= 2.9 is slightly smaller than Tσ |
= 3.0 quantifying scatter of data in the S–N diagram.An alternative method to consider the influence of inclusion size on fatigue lifetime is based on Murakami’s area-model Numbers of cycles to failure are presented as a function of the product of stress amplitude and (area)1/6 in . With stress amplitudes in MPa and ar... |
= 10.7 and C |
= 1.35 × 1038.Scatter of fatigue lifetimes using the parameter Δσ/2(areaINC)1/6 may be quantified using the ratio Tarea of fatigue lifetimes with 90% fracture probability, N90% and 10% fracture probability, N10%. Data points are normalised using Eq. , and a log-normal distribution of lifetimes is assumed. The ratio is ... |
= 2.2 which is smaller than Tσ and TK. From the three methods to present fatigue lifetimes () the parameter Δσ/2(areaINC)1/6 shows the best correlation with the measured fatigue lifetimes.The stress amplitude leading to a fracture probability of 50% at 109 |
cycles in the investigated 18Ni maraging steel is Δσ/2 = 444 MPa, which is 22% of the tensile strength. This percentage may be compared with cyclic tension strengths of other high strength steels measured in the VHCF range. Comparison is possible, however, solely considering comparable loading of specimens. Due to volu... |
cycles at a load ratio of R |
= 0.1 was found for a turbine blade steel with tensile strength of 1000 MPa at 35% of its tensile strength This data survey of VHCF strength under cyclic tension conditions at load ratio R |
= 0 or R |
= 0.1 is summarised in . Cyclic strength of the presently investigated material corresponds well with the other high strength steels included in the survey. Under the investigated conditions, the 18Ni maraging steel tested in the present condition (i.e. tensile strength 2000 MPa, inclusion size areaINC |
⩽ 5.3 μm) shows a correlation of cyclic and tensile strength that is comparable to other high strength steels.Fatigue properties of nitrided 18Ni maraging steel thin sheets have been investigated in the regime of mean lifetimes between 107 and 109 cycles with a further developed ultrasonic fatigue testing method.Mounti... |
cycles.Considering crack initiating inclusions as cracks, their stress intensity ranges are between 1.3 MPa m1/2 and 2.4 MPa m1/2. A granular and homogeneous appearing fracture surface without steps or secondary cracks is formed next to the inclusion with the border at the stress intensity range 4.0 ± 0.2 MPa m1/2. Fis... |
cycles at load ratio R |
= 0.1 is 22% of the tensile strength. This ratio of cyclic to tensile strength for the presently investigated 18Ni maraging steel in the VHCF regime is comparable with other high strength steels tested under similar loading conditions.A multi-scale simulation of tungsten film delamination from silicon substrateTo bridg... |
− |
t basis are given byAt the initiation of decohesion (λd |
= 0), it follows from Eqs. where the normal and tangential tractions, τnb and τtb are obtained from the discontinuous bifurcation analysis. By letting Cm |
= |
τtf/τnf in Eq. , different failure modes can be simulated by utilizing different values of Cm. For example, mode I failure dominates if Cm |
= 10, while mode II failure dominates if Cm |
= 0.1. Mixed failure mode could be simulated by using Cm |
= 1. Well-designed experiments are required to calibrate the value of Cm. The reference traction values, τnf and τtf, can be found from Eq. evaluated at the initiation of bifurcation for given Cm. As can be seen from the above formulations, the discrete model parameters to be determined from the experiments are U0, q ... |
y[0 1 0], |
z[0 0 1]) will therefore be investigated in this study since the decohesion process of single crystal W is of the interest in the current research. By simulating the separation of {1 0 0} planes along the 〈1 0 0〉 direction via MD, a multi-scale decohesion model could be formulated as discussed later.In the MD simulatio... |
y[0 1 0], |
z[0 0 1]).Simulations 1–3 are conducted to study the effect of boundary conditions on the tensile deformation of single crystal W block. shows the corresponding stress–strain curves. Although the stress reaches its peak value at about the strain of 0.34 in both Simulations 1 and 2, the peak stress with PBC in the y-di... |
s−1, 2 × 108 |
s−1 and 2 × 1010 |
s−1, respectively. shows the corresponding stress–strain curves. As can be seen from the figure, the initial elastic modulus of W is almost independent on the strain rate, but the peak stress increases with the strain rate. The dependence of decohesion initiation on the strain rate is mainly due to the dynamic wave ef... |
= |
D1/D2 with D1 and D2 being the characteristic sizes of two similar structures, respectively, f(λ) = |
Y1/Y2 is a dimensionless function with Y1 and Y2 being the material properties at sizes D1 and D2, respectively, and exponent m is an unknown constant.To determine exponent m, a suitable failure criterion must be chosen. For elasto-plasticity with a fixed yield surface which is expressed only in terms of stress or stra... |
= 0 when the material property Y represents the stress or strain. This is known as the case of no size effect on material strength, which is however only true when the size of the structure is within certain range. Indentation tests on single crystal W () have shown that there is certain dependence of material hardness... |
≠ 0 when D |
< 100 μm. No size effect would occur as the structure size is beyond about 100 μm, namely, m |
= 0 when D |
⩾ 100 μm. It seems that the exponent m will change from nonzero to zero when the structure reaches the critical size of about 100 μm.Since there is an effect of strain rate on the strength of crystal W when the strain rate is high, a factor is needed to approximately account for the influence of the strain rate. MD sim... |
s−1. It is therefore assumed in this study that the strength of W obtained with the strain rate of 2 × 108 |
s−1 is rate-insensitive since the specimen sizes are smaller than 28 nm. As can be seen from , the strength of W in Simulation 6, decreases from 24.8 GPa at the rate of 2 × 109 |
s−1 to 22.2 GPa at the rate of 2 × 108 |
s−1 in Simulation 8 with a factor of 22.2/24.8 = 0.895. For the sake of simplicity, all the strengths obtained in Simulations 2, 4–7 with the strain rate of 2 × 109 |
s−1, as shown in , will be multiplied by a factor of 0.895 to approximately calculate the rate-independent strengths at different structure sizes under strain rates in the order of 108 |
s−1.By combining the MD simulation data and the available experimental results, a multi-scale strength model for W is proposed here based on the assumption that the exponent m in the power scaling law must change smoothly when the structure size increases from atomic-scale to macro-scale. presents the MD simulation da... |
= 34.9 GPa atDP |
= 1.6 nm, which is in a reasonable agreement with the maximum tensile strength of 29.5 GPa as reported by using pseudopotential density functional theory, is applied. According to , DM |
= 100 μm is assumed. As a common material property for W, σM |
= 1.5 GPa is adopted in this study. presents the effect of specimen size on the decohesion energy of single crystal W with crystal orientation of (x[1 0 0], |
y[0 1 0], |
z[0 0 1]) under tension. The decohesion energy can be estimated based on the area under the corresponding stress–strain curve within the softening regime in , with a factor of 0.895 being multiplied to approximately account for the rate effect on the strength. As can be seen from , the failure of the W block is an aver... |
= 1 in Eq. , is assumed and Cm is determined through well-designed experiments, a multi-scale decohesion–traction model can then be established for W.Based on the proposed multi-scale simulation procedure, as shown in , a plane-strain problem for simulating the thin film delamination process is designed. The problem co... |
= 10 μm, ht |
= 2.5 μm and hs |
= 5 μm, respectively. The strength of tungsten is σp |
≅ 2.3 GPa based on Eq. by considering the effect of the film thickness. The corresponding yield strength of W is assumed to be σy |
≅ 1.53 GPa. Since the elastic modulus is size-independent, E |
= 411 GPa is employed with Poisson’s ratio ν |
= 0.28 and mass density ρ |
= 15,000 kg/m3. Before the discontinuous bifurcation occurs, the associated von Mises elasto-plasticity model with a linear hardening/softening function is used for W. After bifurcation occurs, the discrete constitutive model is active with U0 |
= 1.67 N/m, q |
= 1.0, and Cm |
= 1.0, 10.0 and 0.1 for mixed mode, mode I and mode II failures, respectively. Since the yield strength of Si is much higher than the strength of W, decohesion is not active inside Si and no size effect is thus considered for Si. An elasto-perfectly-plastic von Mises model is employed for Si, with Young’s modulus E |
= 107 GPa, Poisson’s ratio ν |
= 0.42, mass density ρ |
= 3200 kg/m3, and yield strength σy |
= 8.0 GPa. A step compressive stress of 1.8 GPa is uniformly applied along both ends of tungsten film at the time t |
= 0 to simulate the dynamic failure response.Note that the designed substrate thickness is chosen to be much smaller than that in the real film–substrate problem in order to save computational costs. To reduce the effect of stress wave reflection from the bottom boundary of the substrate on the film failure pattern, a ... |
m long. Initially, one material point per cell is used to discretize both tungsten and silicon. As a result, the interfacial strength would be the average of tungsten and silicon strengths due to the inherent nature of the mapping procedure in the MPM (). To observe the deformation patterns clearly, the deformation fie... |
= 10.0, 0.1 and 1.0, respectively, in the decohesion model for W film. present the failure patterns of the W–Si structure at the time t |
= 2.88 μs with mode I failure, at the time t |
= 1.92 μs with mode II failure, and at the time t |
= 2.88 s with mixed mode failure, respectively. Since the film will be severely damaged at the time t |
= 2.88 μs with mode II failure, only the deformation field of film–substrate structure at t |
= 1.92 μs is shown for mode II failure. As can be seen from , the decohesion might initiate at the top film surface and evolve deeply into the film until reaching the film–substrate interface with mode I and mixed model failures. However, the complete delamination of the film might occur before the film decohesion reac... |
y[0 1 0], |
z[0 0 1]) under tension is conducted by using the EAM potential. The effects of boundary condition, specimen size, number of vacancies, machine precision and strain rate on the stress–strain relation curves are investigated at the atomic level. It is found that shrinking of specimen cross sectional area and rearrangeme... |
m2/kN which corresponds to Sr=1.0–0.9.The maxima of σzz′, σvol′ and (Pz–P0) increase as the degree of saturation (Sr) decreases. indicates the effect of the degree of saturation on vertical seepage force. It reveals that unsaturated soil is more vulnerable to liquefaction. The mechanism for this fragility to liquefact... |
N/m2 but keeps constant along depth. This range is suitable for a wide range of soil masses (. In the shallow zone, Young's modulus E has almost no effect on vertical effective stress σzz′ and vertical seepage force (Pz−P0). The maximum effective stress increases with Young's modulus E. This implies that the seepage fo... |
= |
Tm |
− |
Tl. According to Eq. , the critical nucleus radius decreases with the decreasing of Tl, then the nucleation energy of crystal nucleus reduces and the probability of nucleation increases, which would result in grain and precipitate refinement. Based on the above analysis, the possible reasons for the modification and re... |
= 0.6761 nm) and Mg2Si (cF12 type, a |
= 0.6359 nm) , the effect of adding 0.6 wt.%Sn on the undercooling degree of AZ61–0.7Si alloy is least. Therefore, compared to the adding 0.09 wt.%Sr, adding 0.6 wt.%Sn exhibits relative refinement for the Mg2Si phases, the modification is not obvious. Compared to the adding 0.4 wt.%Sb, the refinement efficiency for th... |
≈ 2/3, for the square lattice pc |
≈ 1/2, and for the triangular lattice pc |
≈ 1/3 and indeed these values match well with those reported in the literature also shows a representative ‘unit cell’ for a continuum model where the central node is connected to 6 adjacent nodes, for which we would again expect pc |
≈ 1/3. This is to say that by increasing the number of bonds attached to each node the percolation threshold can effectively be lowered. This fact can be exploited to manipulate the critical strain at which Si/NiNs nanocomposites begin to respond piezoresistively. By some means, as this material is strained the spatial... |
≈ 1/25.While the introduction of this larger second phase does increase the volume fraction of conductive phase material (with fewer and less expensive particles), the most important effect is that of manipulating the bond length distribution such that the average distance between conductive phase domains is decreased.... |
= NiNs vol %, and y |
= NCCF vol %. The optimization algorithm consisted in the following: (1) measure ɛmax, ɛc, ɛerr; (2) compute the value of the objective function, f; and (3) choose the composition which maximizes the objective function. shows the values of each of the parameters as well as the value of the objective function. From it ... |
= 1.2) in the thickness direction, there is no micro-void found and the slip band and the typical knife edge rupture can be clearly observed on the fracture surface, as shown in c. The decrease of N leads to the localized deformation at the fracture region. Actually, the measured strain is not the fracture strain at th... |
= 1, which has been validated by Hansen , the evolution of dislocation density in the testing specimen is examined and shown in . From the figure, it can be seen that the dislocation density is increased with N. The change of fracture dislocation density (ρc) with N is shown in . There is a linear relationship between ... |
N |
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