scholarly journals Freeze fracturing of elastic porous media: a mathematical model

2015 ◽  
Vol 471 (2175) ◽  
pp. 20140741 ◽  
Author(s):  
I. Vlahou ◽  
M. G. Worster
Keyword(s):  
Mathematical Model ◽  
Fracture Toughness ◽  
Growth Rate ◽  
Unfrozen Water ◽  
Cold Climates ◽  
Porous Rocks ◽  
Rock Fracturing ◽  
Porous Rock ◽  
Freeze Fracturing ◽  
Water Saturated

We present a mathematical model of the fracturing of water-saturated rocks and other porous materials in cold climates. Ice growing inside porous rocks causes large pressures to develop that can significantly damage the rock. We study the growth of ice inside a penny-shaped cavity in a water-saturated porous rock and the consequent fracturing of the medium. Premelting of the ice against the rock, which results in thin films of unfrozen water forming between the ice and the rock, is one of the dominant processes of rock fracturing. We find that the fracture toughness of the rock, the size of pre-existing faults and the undercooling of the environment are the main parameters determining the susceptibility of a medium to fracturing. We also explore the dependence of the growth rates on the permeability and elasticity of the medium. Thin and fast-fracturing cracks are found for many types of rocks. We consider how the growth rate can be limited by the existence of pore ice, which decreases the permeability of a medium, and propose an expression for the effective ‘frozen’ permeability.

Fatigue Crack Growth Rate and Fracture Toughness of API5L X65 in Sweet Environments

2013 ◽  
Author(s):  
Michael A. Tognarelli ◽  
Ramgopal Thodla ◽  
Steven Shademan
Keyword(s):  
Fracture Toughness ◽  
Growth Rate ◽  
Fatigue Crack ◽  
Crack Growth Rate ◽  
Fatigue Crack Growth ◽  
Crack Growth ◽  
Fatigue Crack Growth Rate ◽  
Environmental Conditions ◽  
Initiation Toughness ◽  
Diffusible Hydrogen

Corrosion fatigue and fracture toughness in sour environments of APIX65 5L have typically been studied in relatively severe environments like NACE A and NACE B solutions. There are very limited data in sweet and mildly sour environments that are of interest in various applications. This paper presents fatigue crack growth frequency scans in a range of sweet and mildly sour environments as well as on different microstructures: Parent Pipe, Heat Affected Zone (HAZ) and Weld Center Line (WCL). The fatigue crack growth rate (FCGR) increased with decreasing frequency and reached a plateau value at low frequencies. FCGR in the sweet environments that were investigated did exhibit a frequency dependence (increasing with decreasing frequency) and had plateau FCGR in the range of 10–20× the in-air values. In the mildly sour environments that were investigated, FCGR was found to be about 25 to 30× higher than the in-air values. By comparison, in NACE A environments the FCGR is typically about 50× higher than the in-air values. The FCGRs of parent pipe and HAZ were found to be similar over a range of environments, whereas the WCL FCGR data were consistently lower by about a factor of 2×. The lower FCGR of the WCL is likely due to the lower concentration of diffusible hydrogen in the weld. FCGRs as a function of ΔK (stress integrity factor range) were measured on parent pipe at the plateau frequency. The measured Paris law curves were consistent with the frequency scan data. Rising displacement fracture toughness tests were performed in a range of sweet and sour environments to determine the R-curve behavior. Tests were performed in-situ at a slow K-rate of 0.05Nmm−3/2/s over a range of environmental conditions on parent pipe. The initiation toughness and the slope of the R-curve decreased sharply in the sour environments. The initiation toughness and slopes were largely independent of the notch location as well as environmental conditions. Typical values of initiation toughness were in the range of 90–110N/mm.

scholarly journals Mathematical modelling of thermal stresses within the borehole walls in terms of plasma action

2021 ◽  
Vol 15 (2) ◽  
pp. 63-69
Author(s):  
Anatolii Bulat ◽  
Valentyn Osіnnii ◽  
Andrii Dreus ◽  
Nataliia Osіnnia
Keyword(s):  
Mathematical Model ◽  
Thermal Stresses ◽  
Plasma Jet ◽  
Rock Breaking ◽  
Heating Time ◽  
Borehole Wall ◽  
Heated Layer ◽  
Rock Layer ◽  
Rock Fracturing ◽  
Temperature Plasma

Purpose is the development of a mathematical model to study and describe thermal processes within the borehole wall in terms of plasma-based rock breaking. Methods. The following has been applied: theoretical analysis in the framework of a theory of brittle thermoelasticity breaking, methods of mathematical modeling, and computational experiment. Findings. Brief information on the results of the development of advanced plasma-based technology for borehole reaming for hard mineral mining has been represented. The results of industrial tests of plasma plant of 150-200 kW·s power with plasma-generating gas in the air for hard rock breaking have been represented. The plant and plasma-based technology of borehole reaming were tested in underground conditions of Kryvbas mines while reaming a perimeter hole to drive a ventilation rise in silicate-magnetite quartzites. A mathematical model has been proposed to analyze heat and mechanical fields in the rock during the plasma-based action on the borehole walls. Numerical studies of the temperature dynamics and thermal stresses within the borehole-surrounding rock layer have been carried out. It has been demonstrated that if low-temperature plasma is used (Т = 3500-4000°С), thermal compressing stresses are induced within the thin rock layer; the stresses may exceed the boundary admissible ones. It has been identified that plasma-based effect on the borehole wall makes it possible to create the conditions for intense rock fracturing and breaking. Originality. Solution of a new problem of thermoelastic state of a borehole wall in terms of plasma action has been obtained. The proposed mathematical model has been formulated in a cylindrical coordinate system and considers convective and radiation heat exchange between a plasma jet and a borehole wall. Practical implications. The obtained results make it possible to assess the rock state depending on the plasma jet parameters. The proposed methods of calculations will help carry out research to evaluate breaking parameters (the required heating time, thickness of the heated layer, and approximate spall dimensions) and develop different methods for the breaking process control.

scholarly journals Low temperature mixed-mode debond fracture and fatigue characterisation of foam core sandwich

2018 ◽  
Vol 22 (4) ◽  
pp. 1039-1054 ◽  
Author(s):  
Arash Farshidi ◽  
Christian Berggreen ◽  
Leif A Carlsson
Keyword(s):  
Fracture Toughness ◽  
Growth Rate ◽  
Low Temperature ◽  
Mixed Mode ◽  
Room Temperature ◽  
Sliding Mode ◽  
Fatigue Tests ◽  
Mode I ◽  
Foam Core ◽  
Climatic Chamber

This paper experimentally investigates the effects of low temperature on fracture toughness and fatigue debond growth rate in foam core sandwich composites. Mixed-mode bending specimens were statically and cyclically tested inside a climatic chamber at a low temperature (−20°C) and at room temperature (23°C) as a reference. Testing was conducted in mode I (opening) and mixed-mode I/II (opening-sliding) mode mixities. The fatigue tests results are presented according to the modified Paris–Erdogan relation. Results showed substantial fracture toughness reduction due to low temperature. Low temperature furthermore elevated the cyclic crack growth rate.

scholarly journals Infiltrative instability near topography with implication for the drainage of soluble rocks

2008 ◽  
Vol 12 (6) ◽  
pp. 1285-1293 ◽  
Author(s):  
P. Genthon ◽  
A. Ormond
Keyword(s):  
Growth Rate ◽  
Porous Medium ◽  
Reaction Rate ◽  
Drainage Basin ◽  
Sensitivity Study ◽  
Flow Lines ◽  
Initial Flow ◽  
Underground Channel ◽  
Water Saturated ◽  
Channel Structures

Abstract. We present here numerical modeling of infiltration instability near a topographic edge of a water-saturated porous slice by analogy with a limestone formation devoid of initial heterogeneities such as fractures faults or joints and limited by a vertical cliff. In our runs a first dissolution finger develops near the cliff edge, and ends to intersect it above its mid height. Additional fingers develop upstream with a decreasing growth rate and an increasing width. This results from the decrease of the infiltration velocity with distance to the cliff in our models. A sensitivity study shows that a larger permeability contrast between the fingers and the initial undissolved porous medium produces a larger number of fingers, while increasing the dispersivity (lower Peclet number) produces wider fingers. A slower reaction rate (lower Damkhöler number) produces fingers that follow the initial flow lines, since dissolution occurs simultaneously along the entire finger. These results suggest that alteration by dissolution of limestones or other soluble formations may produce different underground channel structures in the same drainage basin due to local changes of the non-dimensional Pe and Da numbers.

Determining the Scatter in Fatigue Crack Growth Rate Based on Variations in Bulk Property Data

2009 ◽  
Author(s):  
Jeremy S. Daily ◽  
Nathan W. Klingbeil
Keyword(s):  
Fracture Toughness ◽  
Growth Rate ◽  
Fatigue Crack ◽  
Crack Growth Rate ◽  
Fatigue Crack Growth ◽  
Crack Growth ◽  
Fatigue Crack Growth Rate ◽  
Bulk Property ◽  
Plastic Dissipation ◽  
Hardening Modulus

A technique to predict the variability of the Paris regime fatigue crack growth rates in ductile materials based on bulk property (yield strength, hardening modulus, and fracture toughness) variation is presented. The prediction, based on the plastic dissipation in the reversed plastic zone ahead of the crack tip, is carried out for Ti-6Al-4V. The empirical distributions of the bulk properties of Ti-6Al-4V are characterized and directly used in the probabilistic assessment of the fatigue crack growth rate. Since computing the plastic dissipation is a computationally intensive procedure, a novel sampling scheme based on confidence interval minimization was used to generate the empirical distribution of fatigue crack growth rate. This technique also predicts correlation between fatigue crack growth rate and fracture toughness, which may be useful in probabilistic design of turbines.

scholarly journals Fracture Properties of Concrete in Dry Environments with Different Curing Temperatures

2020 ◽  
Vol 10 (14) ◽  
pp. 4734
Author(s):  
Zhengxiang Mi ◽  
Qingbin Li ◽  
Yu Hu ◽  
Chunfeng Liu ◽  
Yu Qiao
Keyword(s):  
Fracture Toughness ◽  
Growth Rate ◽  
Fracture Energy ◽  
Elevated Temperatures ◽  
High Growth ◽  
High Growth Rate ◽  
Growth Speed ◽  
Crossover Effect ◽  
Fracture Properties ◽  
Fracture Parameters

This paper investigated the fracture properties of concrete in dry environments with different curing temperatures (5, 20, 40, and 60 °C). For each curing condition, the key fracture parameters of concrete were tested using wedge splitting specimens at five different ages (3, 7, 14, 28, and 60 d). The results show that in dry environments, the effective fracture toughness and fracture energy of concrete exposed to elevated temperatures increased at a relatively high growth rate at an early age. Nevertheless, the growth speed of effective fracture toughness and fracture energy decreased more quickly at elevated temperatures in the later stages. As a result, the concrete cured at higher temperature exhibited lower ultimate values of fracture parameters, and vice-versa. Namely, a temperature crossover effect was found in the effective fracture toughness and fracture energy of concrete under dry environments. Considering the early growth rate and ultimate values of fracture parameters, the optimum temperature suitable for concrete fracture properties development under dry condition was around 40 °C.

Stability of a Mathematical Model with Piecewise Constant Arguments for Tumor-Immune Interaction Under Drug Therapy

2019 ◽  
Vol 29 (01) ◽  
pp. 1950009 ◽  
Author(s):  
Zonghong Feng ◽  
Xinxing Wu ◽  
Luo Yang
Keyword(s):  
Mathematical Model ◽  
Growth Rate ◽  
Drug Therapy ◽  
Tumor Growth ◽  
Tumor Cells ◽  
Chaotic Behavior ◽  
Sufficient Conditions ◽  
Tumor Growth Rate ◽  
Chaotic Region ◽  
Treatment Parameter

This paper studies a mathematical model for the interaction between tumor cells and Cytotoxic T lymphocytes (CTLs) under drug therapy. We obtain some sufficient conditions for the local and global asymptotical stabilities of the system by using Schur–Cohn criterion and the theory of Lyapunov function. In addition, it is known that the system without any treatment may undergo Neimark–Sacker bifurcation, and there may exist a chaotic region of values of tumor growth rate where the system exhibits chaotic behavior. So it is important to narrow the chaotic region. This may be done by increasing the intensity of the treatment to some extent. Moreover, for a fixed value of tumor growth rate in the chaotic region, a threshold value [Formula: see text] is predicted of the treatment parameter [Formula: see text]. We can see Neimark–Sacker bifurcation of the system when [Formula: see text], and the chaotic behavior for tumor cells ends and the system becomes locally asymptotically stable when [Formula: see text].

scholarly journals Mathematical Modeling of the Fracture Toughness of Phenol Formaldehyde Composites Reinforced with E-Spheres

2009 ◽  
Vol 79-82 ◽  
pp. 1165-1168
Author(s):  
H. Ku ◽  
W. Xiang ◽  
N. Pattarachaiyakoop
Keyword(s):  
Mathematical Modeling ◽  
Mathematical Model ◽  
Fracture Toughness ◽  
Tensile Strength ◽  
Polynomial Interpolation ◽  
Phenol Formaldehyde ◽  
Simple Mathematical Model ◽  
The Mathematical Model ◽  
Conventional Oven ◽  
Lagrange’S Method

The fracture toughness of SLG filled phenolic composites have been determined by short bar tests. It is expensive to prepare the samples for the tests. Therefore, it is necessary to develop a mathematical model that will predict the fracture toughness of particulate filled phenolic composites. Mathematical models for tensile strength, Young’s modulus are available but not for impact strength and fracture toughness. There is no sign that it can be built up from simple mathematical model; polynomial interpolation using Lagrange’s method was therefore employed to generate the fracture toughness model using the data obtained from experiments. From experiments, it was found that the trend of the fracture toughness of the samples cured conventionally was similar to that cured in microwaves; it is therefore possible to predict the fracture toughness of the samples cured in microwaves from shifting the mathematical model generated for fracture toughness of samples post-cured in conventional oven. The shifted model represented the fracture toughness of the samples cured in microwaves vey well.

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