How can I translate (move) a stress field a given distance?

In summary, the conversation discusses the process of modelling a stress field of a dislocation in a 2D plane using MatLab. The dislocation can be rotated at different angles, but is limited to specific angles due to the crystal structure. The code sets up material properties and a grid to calculate the stress at various points. To rotate the dislocation, the x and y values are redefined and the stresses are recalculated. The next step involves moving the dislocation along the plane it sits on, with the distance depending on the angle of rotation. The goal of the exercise is to have multiple dislocations moving in a 2D area and calculating the stress at any point in time. The conversation also mentions successfully running the code with
  • #1
William White
256
80
Hi,
I am modelling the stress field of a dislocation (an extra half line of atoms in a crystal) in a 2D plane using MatLab.

The dislocation can line at different angles. I can rotate the dislocation for any angle; but in relaity the angle is limited by the structure of the crystal: theta is either 0°, 54.7° or 125.2°. i.e. the dislocation must lie on a crystal plane and these are the angles allowed.

My code sets up material properties u; nu and b

They sets up a grid. This gives values of x and y in the 2D plane at which the stress is calculated

The next lines define the magnitude of the stresses Qxx, Qty and Qxy at all values of x and y.

Now if I want to rotate the dislocation, by say 54.7°; x and y are redefined as x2 and y2 and the stresses recalculated as QxxPRIME etc.

The next step of the problem is to move the dislocation by a distance, s, along the plane it sits on. If theta, is say, 0°, which aligns conveniently with the x-axis, then the dislocation should move along the x-axis by a distance s.

If theta is 90°, it moves along the y-axis by a distance s

If theta is 54.7°, it moves along a plane inclined at 54.7, a distance s.
My problem is getting the dislocation to move correctly. The origin 0,0 must stay where it is. The dislocation is centered on the origin. So when x=y=0 then the stresses are infinite - that is the stress at the centre of the dislocation is infinite.

So I am guessing what I cannot do is just add values to x and y, because then x and y will not be zero at the centre of the dislocation.(The goal of the exercise is to have several (in the end, tens of thousands) of dislocations moving along 1D planes in a 2D area and to calculate the entire stress at any point at any time.)If one runs the code twice, with angle at 54.7 and again at 0, one can see the effect of the rotation, which I am happy with.Thank youu = 80000; % Shear modulus, measure in Mpa

nu = 0.3; % Poission’s ratio of material

b = .00025; % Burgers Vector measured in microns

[x,y]=meshgrid(-100:1:100,-100:1:100); % area of grid to which stress field is mapped

angle = 54.7; % angle of slip plane in degrees

theta = angle*pi/180; % angle converted to radians

Qxx = -(u .* b / (2.*pi .* (1-nu))) .* ((y .* (3.*x.^2 +y.^2)) ./ ((x.^2 + y.^2).^2)); % Qxx stress
Qyy = (u .* b / (2.*pi .* (1-nu))) .* ((y .* (x.^2 -y.^2)) ./ ((x.^2 + y.^2).^2)); % Qyy stress
Qxy = (u .* b / (2.*pi .* (1-nu))) .* ((x .* (x.^2 -y.^2)) ./ ((x.^2 + y.^2).^2)); % Qxy stressx2 = x.*cos(theta) + y.*sin(theta); % rotates dislocation

y2 = y.*cos(theta) - x.*sin(theta); % rotates dislocationQxxPRIME = -(u .* b / (2.*pi .* (1-nu))) .* ((y2 .* (3.*x2.^2 +y2.^2)) ./ ((x2.^2 + y2.^2).^2)); % Qyy stress PRIME

QyyPRIME = (u .* b / (2.*pi .* (1-nu))) .* ((y2 .* (x2.^2 -y2.^2)) ./ ((x2.^2 + y2.^2).^2)); % Qyy stress PRIME

QxyPRIME = (u .* b / (2.*pi .* (1-nu))) .* ((x2 .* (x2.^2 -y2.^2)) ./ ((x2.^2 + y2.^2).^2)); % Qxy stress PRIME

contourf(x(1,:),y(:,1)',QxxPRIME)

axis equal
 
  • #3
I've managed to get his working.
 

1. How can I calculate the magnitude of the stress field to be moved?

The magnitude of the stress field to be moved can be calculated using the formula: Stress = Force / Area. This equation takes into account the amount of force applied to a certain area, which determines the intensity of the stress field.

2. What factors should I consider when determining the distance to move the stress field?

When deciding on the distance to move a stress field, it is important to consider the material properties of the object being stressed, the applied force, and the location of any stress concentrations. Other factors that may influence the distance include the desired level of safety or the purpose of the stress analysis.

3. Can I use any software to simulate the movement of a stress field?

Yes, there are various software programs available that can simulate and analyze stress fields. These programs use numerical methods, such as finite element analysis, to calculate the stress distribution and the effects of moving the stress field.

4. Is it possible to move a stress field without causing any damage?

In theory, it is possible to move a stress field without causing any damage. However, this would require precise calculations and control of the applied force and distance. In practical applications, there may be some degree of damage or deformation due to the movement of the stress field.

5. What are some real-life applications of moving stress fields?

Moving stress fields have various applications in engineering and material science. For example, in the design of bridges and buildings, engineers use stress field movement analysis to determine the level of stress on different sections of the structure. This information helps in making design modifications to improve the overall stability and safety of the structure.

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