The difficult part of calculating the stress intensity factor for a specific situation is finding the appropriate value of the dimensionless geometry factor, Y. This geometry factor is dependent on the geometry of the crack, the geometry of the part, and the loading configuration. A classic case is plate with a crack through the center, as shown below:
crack sigma data center 3.0
A residual strength curve for an example case is shown in the figure below. This case is for a 2-inch wide plate with a center through crack and a material with a yield strength of 145 ksi and a plane-strain fracture toughness of 60 ksi*in0.5. The residual strength curve is shown in red. For a given crack size, any stress value above this curve results in failure.
Experimental fatigue crack growth data are usually obtained from tests on simple specimens and are normally presented in terms of fatigue crack propagation rates (da/dN), ΔK and variations in values of R. In cases where σmin is compressive the crack may close during the fatigue cycle and no clear convention for calculating ΔK has peen established. Nevertheless, two popular approaches are:
Resilience is the ability of a system, device, or data center to recover quickly and continue operating after an equipment failure, power outage, or other disruption. It involves the use of redundant components or facilities.
Bones of humans and animals combine two unique features, namely: they are brittle yet have a very high fracture toughness linked to the tortuosity of the crack path and they have the ability to repeatedly heal local fissures such that full recovery of overall mechanical properties is obtained even if the local bone structure is irreversibly changed by the healing process. Here it is demonstrated that Ti2AlC MAX phase metallo-ceramics also having a bone-like hierarchical microstructure and also failing along zig-zag fracture surfaces similarly demonstrate repeated full strength and toughness recovery at room temperature, even though the (high temperature) healing reaction involves the local formation of dense and brittle alumina within the crack. Full recovery of the fracture toughness depends on the healed zone thickness and process zone size formed in the alumina reaction product. A 3-dimensional finite element method (FEM) analysis of the data obtained from a newly designed wedge splitting test allowed full extraction of the local fracture properties of the healed cracks.
Millimetre long cracks in a Ti2AlC sample with a hierarchical bone-like microstructure (see supplementary information Fig. S1) were repeatedly healed (Fig. 1 a-d) by exposure to air at a temperature of 1473 K and measuring the resulting fracture behaviour at room temperature. With the set-up and the data analysis protocol developed quantitative values for the key fracture mechanical properties of the sample (in its pristine and in a healed state) could be determined: its tensile strength (σF) and its fracture toughness (KIC,). The cracks were initiated using a wedge-splitting test configuration (WST) and the force (F) and the crack mouth opening displacement (CMOD) were measured; see Fig. 1a,b (and supplementary information Fig. S2). To obtain the crack length as a function of the CMOD (Fig. 1d), the acoustic emission energy (EAE) was recorded during the enforced crack propagation; see Fig. 1c. The projected crack length was estimated from the cumulative acoustic energy EAE and calibrated against the final crack length as measured with scanning electron microscopy (SEM); see supplementary information Fig. S3.
Acoustic emission was employed to monitor crack extension during the wedge splitting test50. Two microphones (type PICO S/N 4926 and 4928, nominal frequency 500 kHz) were mounted on the WST sample; see Fig. 1b. A Physical Acoustics Ltd. module (PCI-2, c channel 40 MHz 18 bit data-acquisition with ILS40 pre-amplifiers) was used to record the acoustic emission signal. The relation between the crack extension ΔA in chevron-notch and acoustic-emission energy EAE has been established experimentally. The acoustic emission energy EAE of a single wavelet is calculated from the amplitude s(t) of the recorded waveform having a duration T. This amplitude is normalized by the input impedance Ω of the measurement setup used, i. e.:
Meanwhile, the damage process is described the relationship between cohesive-force and crack-opening, which is embedded in the subloading surface model. The cohesive-force embedded constitutive model provides equivalent performance to the traditional cohesive zoned model even in the relatively low numerical cost. In the newly developed EPD constitutive model, the fracture stress σF is prescribed by the combination normal stress σ and shear stress τ on the crack surface, i.e. \(\sigma _\mathrmF=\sqrt\sigma ^2+\alpha \tau ^2\). After a damage initiation, the damage variable evolves by the equivalent strain κ. Note that, the softening induced mesh dependencies are handled by a characteristic length method52.
The above procedure was sequentially applied to analyze the experimental data of the 1st till the 4th healed specimen, respectively. It is noted that, in the FE analysis of the healed specimen, only previously damaged parts corresponding to crack path were replaced with new material properties as target values of the inverse analysis. This allows to evaluate the strength and toughness recovery of healed part.
Before estimating all free parameters listed in Eq. 1, we removed velocity change measurements with uncertainties (two-sigma SDs) larger than 0.1% and applied a 60-day running median filter to the time history of seismic velocity changes obtained through the single-station cross-correlation analysis. This running median filter was required to stabilize temporal change measurements. To evaluate the long-term linear trend of velocity change for each station, we made use of seismic velocity measurements obtained between December 2007 and January 2014. This time period was based on the data availability of the CalEnergy station data. Because station MONP was permanently closed in November 2007, we excluded this station for the long-term velocity change estimate. A nonlinear curve fitting with SciPy (62) was used to determine all free parameters, and the resultant free parameters are summarized in table S1. A goodness of fit to the observed velocity change was evaluated by calculating variance reduction (VR). 2ff7e9595c
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