Computational Science Investigation of Material Mechanics
ETHZ / Master Course in Civil Engineering / FS2022 / exam questions
ETHZ / Master Course in Civil Engineering / FS2022 / exam questions
Fichier Détails
| Cartes-fiches | 65 |
|---|---|
| Langue | English |
| Catégorie | Statique |
| Niveau | Université |
| Crée / Actualisé | 13.10.2022 / 17.01.2023 |
| Lien de web |
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Rayleigh wave speed
In a uniform system, dynamic cracks are theoretically expected to accelerate quickly
to fast speeds, approach the Rayleigh wave speed, but cannot exceed it.
What is the difference between static and dynamic crack growth?
(quasi) static growth --> stable growth
dynamic growth --> unstable growth
What are random fuse models?
An approach to slow brittle fracture that has its roots in statistical physics in the field of critical phenomena and percolation theory.
RFNs can be viewed as a discretization of a continuum dielectric material, a conductor that suffers breakdown.
The individual breakdown thresholds are chosen from a spatially uncorrelated distribution, such as the Weibull distribution.
Realistic crack roughness and crack front shape emerge.
Knowledge of critical phenomena is valid also for fracture.
--> The transition from damage to fracture
But: No real kinematics, dynamics, and strain fields.
What are elements for lattice models and how can they interact?
lattice models: simple kinetic models for material failure
For progressing the understanding of failure processes, simple models are required that focus attention on the processes that are believed to be the most important for a particular system. In this spirit, simple kinetic models are used, with springs, shear springs, or beams in various lattice configurations with a variety of failure laws.
What is LEFM? What are its limitations?
Linear Elastic Fracture Mechanics (LEFM) is an approach that uses linear elasticity theory to analyze the stability of a crack, assuming that the stress-strain behavior of the material is linear and isotropic and is only valid for small deformations and crack sizes.
Limitations:
- Linear elasticity theory assumes that the material behaves linearly and isotropically under stress.
- LEFM is only valid for small deformations and crack sizes.
- It does not take into account the effects of plastic deformation, yielding, or strain hardening.
- It is not suitable for predicting the behavior of brittle materials.
Explain the different fracture modes.
Mode 1 (tension)
Mode 2 (in-plane shear)
Mode 3 (anti-plane shear)
--> The general crack tip stress field is a linear combination of the solutions to the different modes.
How does the stress field look near a sharp crack tip?
What is the J-integral and what are its properties?
The importance of the J-integral in fracture mechanics cannot be overstated.
It is used in many contexts to:
- compute energy flow to the crack tip,
- to estimate crack opening
- and is used as part of failure criteria for ductile materials.
Important properties:
- it is path-independent (any path starting and ending at the crack face gives the same value)
- it is independent of the direction of subsequent crack growth.
(if straight ahead it is equal to the energy release rate J=G)
What are the two main approaches to analyzing the stability of a crack?
The stress intensity factor is a local description
The energy release rate is a global description
Explain different approaches to account for plasticity in fracture mechanics.
Explain how we can use the R-curve to evaluate crack growth.
Fracture propagation criteria
How do we know if a crack propagates in a stable or unstable manner?
We can analyze it with the R-curve.
How does a crack behave under mixed-mode load?
Important question: which way will the crack grow?
One possible approach:
If the material is isotropic and homogeneous,
the crack will propagate in such a way as
to maximize the energy release rate.
Describe challenges in modeling fracture with Finite Element Methods and possible solutions.
Challenges:
- appropriate representation of near-tip stresses (singularity): infinity cannot be represented by computer (mesh)
- crack advancement criterion (increment and orientation)
- adapt discretization for crack increment (mesh)
Explain the basic physical origins of fatigue in materials.
Local stresses in grains (of microstructure) vary considerably and may be much larger than average stress.
Hence, small local slip accumulates over cycles of loading and unloading.
This is particularly true for grains close to the material surface, where constraints against slip are lower.
Fatigue is a material surface phenomenon. (at least initially)
Surface effects that are important for fatigue:
- Surface roughness (from production)
- Surface damages (scratches, dents, ...)
- Surface treatments
Generally, larger defects --> shorter fatigue life
Explain and discuss the S-N curve or Wöhler curve for fatigue.
S-N curve / Wöhler curve are stress-vs-endurance curve
Wöhler curve can provide a probability of failure after a certain number of cycles given applied stress
- some materials(e.g. steel, titanium) have a fatigue limit (endurance limit)
--> an infinite number of cycles do not lead to fatigue failure - other types of materials (e.g. aluminum) do not have a fatigue limit
What are the parameters that affect fatigue life, and do you know empirical laws to describe
them.
How do you account for non-uniform loading history in the fatigue life calculation?
Question:
how to account for the effect of mean stress?
Answer:
many alternative approaches exist
- Smith-Watson-Topper equation
- Morrow correction
- Goodman relationship
- Gerber relationship
- Soderbergrelationship
How can you describe crack growth during fatigue life?
Name observable phenomena of visco-elastic behavior.
What is a storage and loss modulus, how is the loss factor defined?
Strain energy density
Strain energy density is a measure of the energy stored in a material as a result of deformation. Physically, it can be understood as the amount of energy required to deform a unit volume of a material by a unit amount.
strain energy release rate
Strain energy release rate is a measure of the rate at which energy is released from a material as a crack propagates. Physically, it can be understood as the amount of energy released per unit area of newly created crack surface.
When a crack propagates through a material, it creates new surfaces and the atoms and molecules on those surfaces are no longer in contact with each other. This separation of the surfaces requires energy, which is released from the material as strain energy.
Griffith's criterion
from Linear Elastic Fracture Mechanics
A crack will propagate if the energy required to create new surfaces (i.e. the surface energy density) is less than the energy released by the crack as it grows.
\(G \geq G_c\)
