Method and apparatus for investigating toughening mechanisms and crack advance in lightweight materials

A computing device comprising a processor means for receiving input from a user, and output means for displaying an output to the user, the processor comprising means for controlling the computing device to perform the following operational steps:

• (a) prompting the user, with the output means, for information regarding a material having a crack therein;
• (b) receiving the information from the user with the input means;
• (c) selecting an increment of crack advance;
• and
• (d) in accordance with the information received in step (b) and the increment of crack advance selected in step (c), integrating numerically by means of the processor over a region surrounding a tip of the crack to determine an energy change in the region caused by an advance of the crack by the increment of crack advance selected in step (c).

A computing device comprising:

• a processor:
• input means for receiving input from a user;
• and
• output means for displaying an output to the user;
• the processor comprising:
• means for prompting the user, with the output means, for information regarding material having a crack therein;
• means for receiving the information from the user with the input means;
• means for selecting an increment of crack advance;
• and
• means for integrating numerically over a region surrounding a tip of the crack in accordance with the information and the selected increment of crack advance to determine an energy change in the region caused by an advance of the crack by the increment of crack advance.

A series of operational steps to be performed on or by means of a computing device to determine a spatial relationship between (i) at least one region of integration surrounding a crack tip which is in a first material region in a material and (ii) first and second boundaries between the first material region and a second material region in the material, the first boundary being closer to the crack tip than the second boundary, the computing device comprising a processor, an input, and an output, the series of operational steps comprising:

• (a) prompting the user, by means of the output, to enter data comprising material characteristics of portions of the material within the first and second material regions, a thickness d of the second material region, a distance .xi. of the crack tip to the first boundary along a crack path, a radius b around the crack tip in which energy release caused by the crack is to be calculated, and an angle .psi. representing an orientation of the crack path with respect to the first boundary;
• (b) receiving the data from the user by means of the input;
• (c) calculating, in accordance with the data received in step (b), a shortest distance r1 from the crack tip to the first boundary and a shortest distance r2 from the crack tip to the second boundary;
• (d) calculating, in accordance with the material characteristics received in step (b), a radius of plasticity rpl1 of the portion of the material within the first material region and a radius of plasticity rpl2 of the portion of the material within the second material region, wherein the radii b, rpl1, and rpl2 define the at least one region of integration;
• (e) determining whether b<r1 or b>r1;
• (f) if b<r1, determining whether r1<rpl2 or r1>rpl2;
• (g) if b>r1, determining whether r2<rpl2 or r2>rpl2;
• and
• (h) determining the spatial relationship in accordance with results of the determining steps in steps (e)-(g).

A series of operational steps to be performed on or by means of a computing device for locating an intersection point between an ellipse and another curve, the operational steps comprising:

• (a) dividing the ellipse into a plurality of regions, each of the regions being defined by four values boundleft, boundright, boundlower, and boundupper such that said each of the regions of the ellipse consists of points whose x coordinates lie between boundleft and boundright and whose y coordinates lie between boundlower and boundupper;
• (b) determining, by numerical approximation, a numerically approximated intersection point between the ellipse and said another curve, the numerically approximated intersection point having coordinates NRx and Nry;
• and
• (c) for each one of the plurality of regions:
• (i) determining whether boundleft.ltoreq.NRx.ltoreq.boundright;
• (ii) determining whether boundlower.ltoreq.NRy.ltoreq.boundupper;
• (iii) if both of determining steps (c)(i) and (c)(ii) yield affirmative answers, locating the intersection point within that one of the plurality of regions and assigning NRx and NRy as coordinates of the intersection point;
• and
• (iv) if at least one of determining steps (c)(i) and (c)(ii) yields a negative answer, determining that the intersection point lies outside that one of the plurality of regions;
• so that the intersection point is uniquely located in only one of the plurality of regions.