1729:
have however different breaking stresses. All these springs are suspended from a rigid horizontal platform. The load is attached to a horizontal platform, connected to the lower ends of the springs. When this lower platform is absolutely rigid, the load at any point of time is shared equally (irrespective of how many fibers or springs have broken and where) by all the surviving fibers. This mode of load-sharing is called Equal-Load-Sharing mode. The lower platform can also be assumed to have finite rigidity, so that local deformation of the platform occurs wherever springs fail and the surviving neighbor fibers have to share a larger fraction of that transferred from the failed fiber. The extreme case is that of local load-sharing model, where load of the failed spring or fiber is shared (usually equally) by the surviving nearest neighbor fibers.
1716:, fracture toughness can be predicted and improved with crack deflection around second phase particles. Ceramics are usually loaded in compression in everyday use, so the compressive strength is often referred to as the strength; this strength can often exceed that of most metals. However, ceramics are brittle and thus most work done revolves around preventing brittle fracture. Due to how ceramics are manufactured and processed, there are often preexisting defects in the material introduce a high degree of variability in the Mode I brittle fracture. Thus, there is a probabilistic nature to be accounted for in the design of ceramics. The
441:
1786:
of configurations for which stress-intensity solutions have been published, the majority of which were derived from numerical models. The J integral and crack-tip-opening displacement (CTOD) calculations are two more increasingly popular elastic-plastic studies. Additionally, experts are using cutting-edge computational tools to study unique issues such ductile crack propagation, dynamic fracture, and fracture at interfaces. The exponential rise in computational fracture mechanics applications is essentially the result of quick developments in computer technology.
1158:
1794:
2912:
1194:
applied and generally cease propagating when loading is removed. In a ductile material, a crack may progress to a section of the material where stresses are slightly lower and stop due to the blunting effect of plastic deformations at the crack tip. On the other hand, with brittle fracture, cracks spread very rapidly with little or no plastic deformation. The cracks that propagate in a brittle material will continue to grow once initiated.
1135:
1173:(also known as crack formation), crack propagation, and failure, often resulting in a cup-and-cone shaped failure surface. The microvoids nucleate at various internal discontinuities, such as precipitates, secondary phases, inclusions, and grain boundaries in the material. As local stress increases the microvoids grow, coalesce and eventually form a continuous fracture surface. Ductile fracture is typically
350:
53:
399:(UTS), whereas in brittle materials the fracture strength is equivalent to the UTS. If a ductile material reaches its ultimate tensile strength in a load-controlled situation, it will continue to deform, with no additional load application, until it ruptures. However, if the loading is displacement-controlled, the deformation of the material may relieve the load, preventing rupture.
587:
433:
150:
2078:
862:
1672:
Ceramics and inorganic glasses have fracturing behavior that differ those of metallic materials. Ceramics have high strengths and perform well in high temperatures due to the material strength being independent of temperature. Ceramics have low toughness as determined by testing under a tensile load;
1728:
To model fracture of a bundle of fibers, the Fiber Bundle Model was introduced by Thomas Pierce in 1926 as a model to understand the strength of composite materials. The bundle consists of a large number of parallel
Hookean springs of identical length and each having identical spring constants. They
1839:
be more accurate and efficient, meaning they can provide more precise results and do so more quickly than the older methods. Not all traditional methods have been completely replaced, as they can still be useful in certain scenarios, but they may not be the most optimal choice for all applications.
1838:
These methods are used to determine the fracture mechanics parameters using numerical analysis. Some of the traditional methods in computational fracture mechanics, which were commonly used in the past, have been replaced by newer and more advanced techniques. The newer techniques are considered to
1785:
Virtually every area of engineering has been significantly impacted by computers, and fracture mechanics is no exception. Since there are so few actual problems with closed-form analytical solutions, numerical modelling has become an essential tool in fracture analysis. There are literally hundreds
1197:
Crack propagation is also categorized by the crack characteristics at the microscopic level. A crack that passes through the grains within the material is undergoing transgranular fracture. A crack that propagates along the grain boundaries is termed an intergranular fracture. Typically, the bonds
1737:
Failures caused by brittle fracture have not been limited to any particular category of engineered structure. Though brittle fracture is less common than other types of failure, the impacts to life and property can be more severe. The following notable historic failures were attributed to brittle
1193:
The manner in which a crack propagates through a material gives insight into the mode of fracture. With ductile fracture a crack moves slowly and is accompanied by a large amount of plastic deformation around the crack tip. A ductile crack will usually not propagate unless an increased stress is
1632:
Following this test, the sample can then be reoriented such that further loading of a load (F) will extend this crack and thus a load versus sample deflection curve can be obtained. With this curve, the slope of the linear portion, which is the inverse of the compliance of the material, can be
1165:
Because ductile rupture involves a high degree of plastic deformation, the fracture behavior of a propagating crack as modelled above changes fundamentally. Some of the energy from stress concentrations at the crack tips is dissipated by plastic deformation ahead of the crack as it propagates.
1113:
The basic sequence in a typical brittle fracture is: introduction of a flaw either before or after the material is put in service, slow and stable crack propagation under recurring loading, and sudden rapid failure when the crack reaches critical crack length based on the conditions defined by
1184:
The microvoid coalescence results in a dimpled appearance on the fracture surface. The dimple shape is heavily influenced by the type of loading. Fracture under local uniaxial tensile loading usually results in formation of equiaxed dimples. Failures caused by shear will produce elongated or
402:
The statistics of fracture in random materials have very intriguing behavior, and was noted by the architects and engineers quite early. Indeed, fracture or breakdown studies might be the oldest physical science studies, which still remain intriguing and very much alive.
1789:
Most used computational numerical methods are finite element and boundary integral equation methods. Other methods include stress and displacement matching, element crack advance in which latter two come under
Traditional Methods in Computational Fracture Mechanics.
3106:
1198:
between material grains are stronger at room temperature than the material itself, so transgranular fracture is more likely to occur. When temperatures increase enough to weaken the grain bonds, intergranular fracture is the more common fracture mode.
681:
460:
takes place before fracture. Brittle fracture typically involves little energy absorption and occurs at high speeds—up to 2,133.6 m/s (7,000 ft/s) in steel. In most cases brittle fracture will continue even when loading is discontinued.
1330:
411:
more than 400 years ago. This is the manifestation of the extreme statistics of failure (bigger sample volume can have larger defects due to cumulative fluctuations where failures nucleate and induce lower strength of the sample).
1058:
576:
407:, more than 500 years ago, observed that the tensile strengths of nominally identical specimens of iron wire decrease with increasing length of the wires (see e.g., for a recent discussion). Similar observations were made by
325:
occur after visible deformation. Fracture strength, or breaking strength, is the stress when a specimen fails or fractures. The detailed understanding of how a fracture occurs and develops in materials is the object of
1125:
Under certain conditions, ductile materials can exhibit brittle behavior. Rapid loading, low temperature, and triaxial stress constraint conditions may cause ductile materials to fail without prior deformation.
1185:
parabolic shaped dimples that point in opposite directions on the matching fracture surfaces. Finally, tensile tearing produces elongated dimples that point in the same direction on matching fracture surfaces.
1122:), nominal stress level (σ), and introduced flaw size (a). Residual stresses, temperature, loading rate, and stress concentrations also contribute to brittle fracture by influencing the three primary factors.
293:. The fracture of a solid usually occurs due to the development of certain displacement discontinuity surfaces within the solid. If a displacement develops perpendicular to the surface, it is called a
1720:
predicts the survival probability of a fraction of samples with a certain volume that survive a tensile stress sigma, and is often used to better assess the success of a ceramic in avoiding fracture.
1806:
The structures are divided into discrete elements of 1-D beam, 2-D plane stress or plane strain, 3-D bricks or tetrahedron types. The continuity of the elements are enforced using the nodes.
1951:
A simple load-controlled tensile situation would be to support a specimen from above, and hang a weight from the bottom end. The load on the specimen is then independent of its deformation.
916:
1702:
1662:
1627:
1468:
1235:
1409:
857:{\displaystyle \sigma _{\mathrm {elliptical\ crack} }=\sigma _{\mathrm {applied} }\left(1+2{\sqrt {\frac {a}{\rho }}}\right)=2\sigma _{\mathrm {applied} }{\sqrt {\frac {a}{\rho }}}}
1110:, the phenomenon of crack propagation faster than the speed of sound in a material. This phenomenon was recently also verified by experiment of fracture in rubber-like materials.
1378:
2190:
1552:
1519:
1433:
273:
1254:
1154:
of ductile materials loaded in tension. The extensive plasticity causes the crack to propagate slowly due to the absorption of a large amount of energy before fracture.
1596:
1574:
1490:
2137:
636:
1081:
960:
669:
2542:
2391:
1101:
938:
610:
2801:
1822:. With given boundary conditions, the stresses, strains, and displacements within the body can all theoretically be solved for, along with the tractions on S
972:
495:
1964:
to the ends of a specimen. As the jack extends, it controls the displacement of the specimen; the load on the specimen is dependent on the deformation.
2572:
A. Garcimartin, A. Guarino, L. Bellon and S. Cilberto (1997) "Statistical
Properties of Fracture Precursors". Physical Review Letters, 79, 3202 (1997)
1248:
By performing the compact tension and three-point flexural tests, one is able to determine the fracture toughness through the following equation:
266:
2518:
2367:
2292:
2643:
3087:
1237:), so fracture testing is often done to determine this. The two most widely used techniques for determining fracture toughness are the
2267:
2173:
2583:
2567:
2431:
2334:
2215:
C. H. Chen; H. P. Zhang; J. Niemczura; K. Ravi-Chandar; M. Marder (November 2011). "Scaling of crack propagation in rubber sheets".
2011:
259:
136:
3125:
2794:
381:
2121:
1886:
1750:
74:
1206:
Fracture in materials is studied and quantified in multiple ways. Fracture is largely determined by the fracture toughness (
3186:
3161:
1871:
1866:
1633:
obtained. This is then used to derive f(c/a) as defined above in the equation. With the knowledge of all these variables,
2602:
289:
is the appearance of a crack or complete separation of an object or material into two or more pieces under the action of
3067:
117:
3166:
2787:
2763:
222:
89:
3176:
2891:
212:
874:
63:
3156:
1926:
1238:
396:
357:
227:
70:
39:
1525:
to better emulate a crack tip found in real-world materials. Cyclical prestressing the sample can then induce a
96:
3191:
1242:
2901:
2636:
1157:
389:
1676:
1636:
1601:
1442:
1209:
2046:"Story of the Developments in Statistical Physics of Fracture, Breakdown and Earthquake: A Personal Account"
1385:
485:
The fracture strength (or micro-crack nucleation stress) of a material was first theoretically estimated by
232:
3171:
1174:
202:
103:
2448:
1341:
448:
of a bicycle, where the bright areas display a brittle fracture, and the dark areas show fatigue fracture
1911:
1901:
1170:
1147:
1793:
2224:
1906:
1881:
1814:
In this method, the surface is divided into two regions: a region where displacements are specified S
1743:
1717:
1532:
1499:
486:
457:
421:
85:
1325:{\displaystyle \mathrm {K_{c}} =\sigma _{\mathrm {F} }{\sqrt {\pi \mathrm {c} }}\mathrm {f\ (c/a)} }
3135:
3095:
2879:
2629:
1916:
1522:
1493:
1114:
fracture mechanics. Brittle fracture may be avoided by controlling three primary factors: material
1107:
479:
247:
217:
182:
1416:
671:
is the micro-crack length (or equilibrium distance between atomic centers in a crystalline solid).
3181:
3073:
2973:
2810:
2712:
2536:
2385:
2240:
2131:
1896:
1876:
1526:
1115:
466:
327:
207:
187:
31:
613:
3100:
3000:
2995:
2936:
2926:
2864:
2681:
2579:
2563:
2524:
2514:
2468:
2427:
2373:
2363:
2340:
2330:
2298:
2288:
2263:
2169:
2117:
2067:
2007:
1705:
1579:
1557:
1473:
404:
177:
621:
420:
There are two types of fractures: brittle and ductile fractures respectively without or with
2951:
2758:
2702:
2616:
2460:
2232:
2057:
1713:
1151:
349:
290:
2911:
1066:
945:
647:
2874:
2606:
1921:
1709:
675:
On the other hand, a crack introduces a stress concentration modeled by Inglis's equation
475:
408:
339:
2228:
3062:
3057:
2990:
2748:
1773:
1086:
1053:{\displaystyle \sigma _{\mathrm {fracture} }={\sqrt {\frac {E\gamma \rho }{4ar_{o}}}}.}
923:
639:
595:
471:
362:
3107:
How Long Is the Coast of
Britain? Statistical Self-Similarity and Fractional Dimension
1492:
must be precisely measured. This is done by taking the test piece with its fabricated
1150:) takes place before fracture. The terms "rupture" and "ductile rupture" describe the
380:
Fracture strength, also known as breaking strength, is the stress at which a specimen
110:
3150:
3052:
3047:
2717:
2464:
1961:
1754:
237:
35:
2621:
1134:
2963:
2886:
2869:
2244:
2236:
1960:
A simple displacement-controlled tensile situation would be to attach a very stiff
1891:
1830:. It is a very powerful technique to find the unknown tractions and displacements.
1769:
1758:
385:
571:{\displaystyle \sigma _{\mathrm {theoretical} }={\sqrt {\frac {E\gamma }{r_{o}}}}}
17:
3081:
3039:
2958:
2854:
2849:
2671:
1765:
1178:
474:
acting normal to crystallographic planes with low bonding (cleavage planes). In
453:
343:
311:
52:
2082:
338:"Breaking strain" redirects here. For the short story by Arthur C. Clarke, see
3028:
3023:
2941:
2844:
2707:
2686:
2676:
2666:
2652:
2508:
2114:
Fracture and fatigue control in structures: applications of fracture mechanics
2062:
2045:
586:
30:
This article is about the science of fractures. For predicting fractures, see
2528:
2472:
2377:
2324:
2302:
2071:
3130:
3033:
2768:
2753:
2738:
2344:
1797:
Fine Mesh done in
Rectangular area in Ansys software (Finite Element Method)
1143:
445:
440:
432:
172:
149:
1138:
Schematic representation of the steps in ductile fracture (in pure tension)
2859:
1842:
Some of the traditional methods in computational fracture mechanics are:
167:
2362:. Wright, Wendelin J. (Seventh ed.). Boston, MA. pp. 236–237.
2985:
2980:
2968:
2946:
2931:
2839:
2733:
2611:
2077:
1931:
192:
1380:
is an empirically-derived equation to capture the test sample geometry
1181:
slip can cause the shear lip characteristic of cup and cone fracture.
2779:
2191:"Stresses in a plate due to the presence of cracks and sharp corners"
590:
Brittle cleavage fracture surface from a scanning electron microscope
2405:
An improved semi-analytical solution for stress at round-tip notches
2404:
384:
via fracture. This is usually determined for a given specimen by a
3018:
1792:
1156:
1133:
585:
439:
431:
348:
148:
2896:
2834:
2829:
478:, by contrast, the lack of a crystalline structure results in a
392:(see image). The final recorded point is the fracture strength.
242:
2783:
2625:
2588:
Peter Rhys Lewis, Colin Gagg, Ken
Reynolds, CRC Press (2004),
46:
2081:
Text was copied from this source, which is available under a
1169:
The basic steps in ductile fracture are microvoid formation,
1540:
1529:
which extends the crack from the fabricated notch length of
1507:
395:
Ductile materials have a fracture strength lower than the
301:; if a displacement develops tangentially, it is called a
2002:
Degarmo, E. Paul; Black, J T.; Kohser, Ronald A. (2003),
1704:
values that are ~5% of that found in metals. However, as
482:, with cracks proceeding normal to the applied tension.
464:
In brittle crystalline materials, fracture can occur by
321:
occur without any apparent deformation before fracture.
2510:
Fracture mechanics : fundamentals and applications
1834:
Traditional methods in computational fracture mechanics
153:
Ductile failure of a metallic specimen strained axially
2083:
Creative
Commons Attribution 4.0 International License
1679:
1639:
1604:
1582:
1560:
1535:
1502:
1476:
1445:
1212:
1419:
1388:
1344:
1257:
1089:
1069:
975:
948:
926:
877:
684:
650:
624:
598:
498:
1103:) both lower the fracture strength of the material.
3118:
3011:
2919:
2817:
2726:
2695:
2659:
2577:
Materials
Science and Engineering: An Introduction.
2198:
77:. Unsourced material may be challenged and removed.
2285:Materials science and engineering: an introduction
2039:
2037:
1696:
1656:
1621:
1590:
1568:
1546:
1513:
1484:
1462:
1427:
1403:
1372:
1324:
1229:
1095:
1075:
1052:
954:
932:
910:
856:
663:
630:
604:
570:
1746:in 1919, New Jersey molasses tank failure in 1973
1598:is used in the above equations for determining
2166:Fatigue and fracture: understanding the basics
2795:
2637:
267:
27:Split of materials or structures under stress
8:
2590:Forensic Materials Engineering: Case Studies
2136:: CS1 maint: multiple names: authors list (
2116:(3 ed.). West Conshohocken, Pa.: ASTM.
1161:Ductile fracture surface of 6061-T6 aluminum
962:is the radius of curvature at the crack tip.
911:{\displaystyle \sigma _{\mathrm {applied} }}
353:Stress vs. strain curve typical of aluminum
2447:Faber, K. T.; Evans, A. G. (1 April 1983).
2417:
2415:
2413:
2168:. Materials Park, Ohio: ASM International.
2802:
2788:
2780:
2644:
2630:
2622:
2612:Fracture and Reconstruction of a Clay Bowl
2541:: CS1 maint: location missing publisher (
2390:: CS1 maint: location missing publisher (
2159:
2157:
2155:
2153:
2151:
2149:
2147:
2112:Rolfe, John M. Barsom, Stanley T. (1999).
966:Putting these two equations together gets
274:
260:
156:
2287:(8th ed.). Wiley. pp. 236–237.
2061:
1997:
1995:
1818:and region with tractions are specified S
1757:collapse in 1967, partial failure of the
1687:
1686:
1681:
1678:
1647:
1646:
1641:
1638:
1612:
1611:
1606:
1603:
1583:
1581:
1561:
1559:
1536:
1534:
1503:
1501:
1477:
1475:
1453:
1452:
1447:
1444:
1420:
1418:
1394:
1393:
1387:
1358:
1345:
1343:
1310:
1297:
1290:
1285:
1278:
1277:
1263:
1258:
1256:
1220:
1219:
1214:
1211:
1146:fracture, extensive plastic deformation (
1088:
1068:
1037:
1012:
981:
980:
974:
947:
925:
883:
882:
876:
842:
817:
816:
789:
750:
749:
690:
689:
683:
655:
649:
623:
597:
559:
544:
504:
503:
497:
137:Learn how and when to remove this message
2360:The science and engineering of materials
2050:Reports in Advances of Physical Sciences
2029:Civil. Eng. and Env. Syst. 18 (2000) 243
2004:Materials and Processes in Manufacturing
1697:{\textstyle \mathrm {K} _{\mathrm {c} }}
1657:{\textstyle \mathrm {K} _{\mathrm {c} }}
1622:{\textstyle \mathrm {K} _{\mathrm {c} }}
1463:{\textstyle \mathrm {K} _{\mathrm {c} }}
1230:{\textstyle \mathrm {K} _{\mathrm {c} }}
2329:. R. J. H. Wanhill. London: E. Arnold.
2107:
2105:
2103:
2101:
2099:
2097:
2095:
2093:
2091:
2044:Chakrabarti, Bikas K. (December 2017).
1977:
1944:
159:
2534:
2449:"Crack deflection processes—I. Theory"
2383:
2129:
1404:{\displaystyle \sigma _{\mathrm {F} }}
2502:
2500:
2498:
2496:
2318:
2316:
2314:
2312:
1810:The boundary integral equation method
1106:Recently, scientists have discovered
7:
2358:Askeland, Donald R. (January 2015).
940:is half the length of the crack, and
342:. For the novel by Paul Preuss, see
75:adding citations to reliable sources
3088:The Chemical Basis of Morphogenesis
2006:(9th ed.), Wiley, p. 32,
1373:{\displaystyle \mathrm {f\ (c/a)} }
2575:Callister, Jr., William D. (2002)
2283:Callister, William D. Jr. (2018).
1688:
1682:
1648:
1642:
1613:
1607:
1584:
1562:
1537:
1504:
1478:
1454:
1448:
1421:
1395:
1363:
1355:
1346:
1315:
1307:
1298:
1291:
1279:
1264:
1260:
1221:
1215:
1003:
1000:
997:
994:
991:
988:
985:
982:
902:
899:
896:
893:
890:
887:
884:
836:
833:
830:
827:
824:
821:
818:
769:
766:
763:
760:
757:
754:
751:
736:
733:
730:
727:
724:
718:
715:
712:
709:
706:
703:
700:
697:
694:
691:
535:
532:
529:
526:
523:
520:
517:
514:
511:
508:
505:
25:
2653:Types and processes of weathering
2910:
2513:(3rd ed.). Boca Raton, FL.
2488:J. Textile Indust. 17 (1926) 355
2424:Mechanical behavior of materials
2076:
1846:Stress and displacement matching
1781:Computational fracture mechanics
1547:{\textstyle \mathrm {c\prime } }
1514:{\textstyle \mathrm {c\prime } }
51:
62:needs additional citations for
1887:Forensic materials engineering
1668:Ceramics and inorganic glasses
1366:
1352:
1318:
1304:
373:Offset strain (typically 0.2%)
1:
2764:Factors of polymer weathering
2426:(3nd ed.), McGraw Hill,
1987:Mechanics of Brittle Fracture
1872:Environmental stress fracture
1867:Environmental stress cracking
2465:10.1016/0001-6160(83)90046-9
2422:Courtney, Thomas H. (2000),
2164:Campbell, F.C., ed. (2012).
1428:{\displaystyle \mathrm {c} }
322:
318:
2189:Inglis, Charles E. (1913).
2027:Lund, J. R.; Bryne, J. P.,
1411:is the fracture stress, and
1083:) and large defects (large
223:Metal-induced embrittlement
3208:
2262:(2nd ed.). Springer.
2237:10.1209/0295-5075/96/36009
1826:and the displacements on S
337:
213:Liquid metal embrittlement
34:. For bone fractures, see
29:
3068:D'Arcy Wentworth Thompson
2908:
2063:10.1142/S242494241750013X
1927:Stress corrosion cracking
1802:The finite element method
1591:{\textstyle \mathrm {c} }
1569:{\textstyle \mathrm {c} }
1485:{\textstyle \mathrm {c} }
1239:three-point flexural test
436:Brittle fracture in glass
397:ultimate tensile strength
367:Proportional limit stress
358:Ultimate tensile strength
228:Stress corrosion cracking
40:Fracture (disambiguation)
2603:Component Failure Museum
2507:Anderson, T. L. (2005).
1664:can then be calculated.
444:Fracture of an aluminum
160:Mechanical failure modes
1855:Virtual crack extension
1849:Elemental crack advance
1753:span collapse in 1962,
1177:and deformation due to
631:{\displaystyle \gamma }
233:Sulfide stress cracking
2323:Ewalds, H. L. (1985).
2258:Perez, Nestor (2016).
1798:
1698:
1658:
1623:
1592:
1570:
1548:
1515:
1486:
1464:
1429:
1405:
1374:
1326:
1231:
1162:
1139:
1097:
1077:
1054:
956:
934:
918:is the loading stress,
912:
858:
665:
632:
606:
591:
572:
456:fracture, no apparent
449:
437:
377:
203:Hydrogen embrittlement
154:
38:. For other uses, see
2902:Widmanstätten pattern
2561:Mechanical Metallurgy
2559:Dieter, G. E. (1988)
1912:Microvoid coalescence
1902:Fracture (mineralogy)
1796:
1772:during World War II,
1699:
1673:often, ceramics have
1659:
1624:
1593:
1571:
1549:
1516:
1487:
1465:
1439:To accurately attain
1430:
1406:
1375:
1327:
1232:
1171:microvoid coalescence
1160:
1137:
1098:
1078:
1076:{\displaystyle \rho }
1055:
957:
955:{\displaystyle \rho }
935:
913:
859:
666:
664:{\displaystyle r_{o}}
633:
607:
589:
573:
443:
435:
352:
152:
3187:Plasticity (physics)
3162:Elasticity (physics)
1907:Gilbert tessellation
1882:Forensic engineering
1744:Great Molasses Flood
1718:Weibull distribution
1677:
1637:
1602:
1580:
1558:
1533:
1521:and sharpening this
1500:
1474:
1443:
1435:is the crack length.
1417:
1386:
1342:
1255:
1210:
1087:
1067:
1063:Sharp cracks (small
973:
946:
924:
875:
682:
648:
622:
596:
496:
487:Alan Arnold Griffith
295:normal tensile crack
71:improve this article
3136:Mathematics and art
3126:Pattern recognition
3096:Aristid Lindenmayer
2696:Physical weathering
2660:Chemical weathering
2229:2011EL.....9636009C
2217:Europhysics Letters
1917:Notch (engineering)
1852:Contour integration
1108:supersonic fracture
480:conchoidal fracture
458:plastic deformation
422:plastic deformation
390:stress–strain curve
388:, which charts the
218:Mechanical overload
3167:Fracture mechanics
3074:On Growth and Form
2974:Logarithmic spiral
2811:Patterns in nature
2326:Fracture mechanics
2260:Fracture Mechanics
1985:Cherepanov, G.P.,
1897:Fracture (geology)
1877:Fatigue (material)
1799:
1751:King Street Bridge
1742:Pressure vessels:
1694:
1654:
1619:
1588:
1566:
1544:
1511:
1482:
1460:
1425:
1401:
1370:
1322:
1227:
1163:
1140:
1116:fracture toughness
1093:
1073:
1050:
952:
930:
908:
864:(For sharp cracks)
854:
661:
628:
602:
592:
568:
450:
438:
424:prior to failure.
378:
328:fracture mechanics
155:
32:Fracture mechanics
3177:Materials science
3144:
3143:
3101:Benoît Mandelbrot
3001:Self-organization
2937:Natural selection
2927:Pattern formation
2777:
2776:
2682:Mineral hydration
2605:(archived 2016),
2520:978-1-4200-5821-5
2453:Acta Metallurgica
2369:978-1-305-07676-1
2294:978-1-119-40539-9
1351:
1303:
1295:
1096:{\displaystyle a}
1045:
1044:
933:{\displaystyle a}
852:
851:
799:
798:
723:
605:{\displaystyle E}
566:
565:
470:as the result of
405:Leonardo da Vinci
323:Ductile fractures
319:Brittle fractures
284:
283:
178:Corrosion fatigue
147:
146:
139:
121:
18:Fracture strength
16:(Redirected from
3199:
3157:Building defects
2952:Sexual selection
2914:
2804:
2797:
2790:
2781:
2759:Space weathering
2703:Frost weathering
2646:
2639:
2632:
2623:
2617:Ductile fracture
2547:
2546:
2540:
2532:
2504:
2491:
2490:
2483:
2477:
2476:
2444:
2438:
2437:
2419:
2408:
2402:
2396:
2395:
2389:
2381:
2355:
2349:
2348:
2320:
2307:
2306:
2280:
2274:
2273:
2255:
2249:
2248:
2212:
2206:
2205:
2195:
2186:
2180:
2179:
2161:
2142:
2141:
2135:
2127:
2109:
2086:
2080:
2075:
2065:
2041:
2032:
2031:
2024:
2018:
2017:
1999:
1990:
1989:
1982:
1965:
1958:
1952:
1949:
1703:
1701:
1700:
1695:
1693:
1692:
1691:
1685:
1663:
1661:
1660:
1655:
1653:
1652:
1651:
1645:
1628:
1626:
1625:
1620:
1618:
1617:
1616:
1610:
1597:
1595:
1594:
1589:
1587:
1575:
1573:
1572:
1567:
1565:
1553:
1551:
1550:
1545:
1543:
1520:
1518:
1517:
1512:
1510:
1491:
1489:
1488:
1483:
1481:
1469:
1467:
1466:
1461:
1459:
1458:
1457:
1451:
1434:
1432:
1431:
1426:
1424:
1410:
1408:
1407:
1402:
1400:
1399:
1398:
1379:
1377:
1376:
1371:
1369:
1362:
1349:
1331:
1329:
1328:
1323:
1321:
1314:
1301:
1296:
1294:
1286:
1284:
1283:
1282:
1269:
1268:
1267:
1236:
1234:
1233:
1228:
1226:
1225:
1224:
1218:
1152:ultimate failure
1102:
1100:
1099:
1094:
1082:
1080:
1079:
1074:
1059:
1057:
1056:
1051:
1046:
1043:
1042:
1041:
1025:
1014:
1013:
1008:
1007:
1006:
961:
959:
958:
953:
939:
937:
936:
931:
917:
915:
914:
909:
907:
906:
905:
863:
861:
860:
855:
853:
844:
843:
841:
840:
839:
805:
801:
800:
791:
790:
774:
773:
772:
741:
740:
739:
721:
670:
668:
667:
662:
660:
659:
637:
635:
634:
629:
616:of the material,
611:
609:
608:
603:
577:
575:
574:
569:
567:
564:
563:
554:
546:
545:
540:
539:
538:
476:amorphous solids
276:
269:
262:
157:
142:
135:
131:
128:
122:
120:
79:
55:
47:
21:
3207:
3206:
3202:
3201:
3200:
3198:
3197:
3196:
3192:Solid mechanics
3147:
3146:
3145:
3140:
3114:
3007:
2915:
2906:
2813:
2808:
2778:
2773:
2722:
2713:Thermal fatigue
2691:
2655:
2650:
2607:Open University
2599:
2556:
2554:Further reading
2551:
2550:
2533:
2521:
2506:
2505:
2494:
2486:Pierce, F. T.,
2485:
2484:
2480:
2446:
2445:
2441:
2434:
2421:
2420:
2411:
2407:, a closer look
2403:
2399:
2382:
2370:
2357:
2356:
2352:
2337:
2322:
2321:
2310:
2295:
2282:
2281:
2277:
2270:
2257:
2256:
2252:
2214:
2213:
2209:
2193:
2188:
2187:
2183:
2176:
2163:
2162:
2145:
2128:
2124:
2111:
2110:
2089:
2043:
2042:
2035:
2026:
2025:
2021:
2014:
2001:
2000:
1993:
1984:
1983:
1979:
1974:
1969:
1968:
1959:
1955:
1950:
1946:
1941:
1936:
1922:Season cracking
1862:
1836:
1829:
1825:
1821:
1817:
1812:
1804:
1783:
1735:
1726:
1680:
1675:
1674:
1670:
1640:
1635:
1634:
1605:
1600:
1599:
1578:
1577:
1556:
1555:
1531:
1530:
1498:
1497:
1472:
1471:
1470:, the value of
1446:
1441:
1440:
1415:
1414:
1389:
1384:
1383:
1340:
1339:
1273:
1259:
1253:
1252:
1243:compact tension
1213:
1208:
1207:
1204:
1191:
1189:Characteristics
1132:
1121:
1085:
1084:
1065:
1064:
1033:
1026:
1015:
976:
971:
970:
944:
943:
922:
921:
878:
873:
872:
812:
779:
775:
745:
685:
680:
679:
651:
646:
645:
620:
619:
614:Young's modulus
594:
593:
555:
547:
499:
494:
493:
430:
418:
409:Galileo Galilei
376:
347:
340:Breaking Strain
336:
280:
143:
132:
126:
123:
80:
78:
68:
56:
43:
28:
23:
22:
15:
12:
11:
5:
3205:
3203:
3195:
3194:
3189:
3184:
3179:
3174:
3169:
3164:
3159:
3149:
3148:
3142:
3141:
3139:
3138:
3133:
3128:
3122:
3120:
3116:
3115:
3113:
3112:
3111:
3110:
3098:
3093:
3092:
3091:
3079:
3078:
3077:
3065:
3063:Wilson Bentley
3060:
3058:Joseph Plateau
3055:
3050:
3045:
3044:
3043:
3031:
3026:
3021:
3015:
3013:
3009:
3008:
3006:
3005:
3004:
3003:
2998:
2996:Plateau's laws
2993:
2991:Fluid dynamics
2988:
2978:
2977:
2976:
2971:
2966:
2956:
2955:
2954:
2949:
2944:
2939:
2929:
2923:
2921:
2917:
2916:
2909:
2907:
2905:
2904:
2899:
2894:
2889:
2884:
2883:
2882:
2877:
2872:
2867:
2857:
2852:
2847:
2842:
2837:
2832:
2827:
2821:
2819:
2815:
2814:
2809:
2807:
2806:
2799:
2792:
2784:
2775:
2774:
2772:
2771:
2766:
2761:
2756:
2751:
2746:
2741:
2736:
2730:
2728:
2727:Related topics
2724:
2723:
2721:
2720:
2715:
2710:
2705:
2699:
2697:
2693:
2692:
2690:
2689:
2684:
2679:
2674:
2669:
2663:
2661:
2657:
2656:
2651:
2649:
2648:
2641:
2634:
2626:
2620:
2619:
2614:
2609:
2598:
2597:External links
2595:
2594:
2593:
2586:
2573:
2570:
2555:
2552:
2549:
2548:
2519:
2492:
2478:
2459:(4): 565–576.
2439:
2432:
2409:
2397:
2368:
2350:
2335:
2308:
2293:
2275:
2269:978-3319249971
2268:
2250:
2207:
2181:
2175:978-1615039760
2174:
2143:
2122:
2087:
2056:(4): 1750013.
2033:
2019:
2012:
1991:
1976:
1975:
1973:
1970:
1967:
1966:
1953:
1943:
1942:
1940:
1937:
1935:
1934:
1929:
1924:
1919:
1914:
1909:
1904:
1899:
1894:
1889:
1884:
1879:
1874:
1869:
1863:
1861:
1858:
1857:
1856:
1853:
1850:
1847:
1835:
1832:
1827:
1823:
1819:
1815:
1811:
1808:
1803:
1800:
1782:
1779:
1778:
1777:
1774:SS Schenectady
1762:
1747:
1734:
1731:
1725:
1722:
1690:
1684:
1669:
1666:
1650:
1644:
1615:
1609:
1586:
1564:
1542:
1539:
1509:
1506:
1480:
1456:
1450:
1437:
1436:
1423:
1412:
1397:
1392:
1381:
1368:
1365:
1361:
1357:
1354:
1348:
1333:
1332:
1320:
1317:
1313:
1309:
1306:
1300:
1293:
1289:
1281:
1276:
1272:
1266:
1262:
1223:
1217:
1203:
1200:
1190:
1187:
1131:
1128:
1119:
1092:
1072:
1061:
1060:
1049:
1040:
1036:
1032:
1029:
1024:
1021:
1018:
1011:
1005:
1002:
999:
996:
993:
990:
987:
984:
979:
964:
963:
951:
941:
929:
919:
904:
901:
898:
895:
892:
889:
886:
881:
866:
865:
850:
847:
838:
835:
832:
829:
826:
823:
820:
815:
811:
808:
804:
797:
794:
788:
785:
782:
778:
771:
768:
765:
762:
759:
756:
753:
748:
744:
738:
735:
732:
729:
726:
720:
717:
714:
711:
708:
705:
702:
699:
696:
693:
688:
673:
672:
658:
654:
643:
640:surface energy
627:
617:
601:
579:
578:
562:
558:
553:
550:
543:
537:
534:
531:
528:
525:
522:
519:
516:
513:
510:
507:
502:
472:tensile stress
429:
426:
417:
414:
375:
374:
371:
368:
365:
363:Yield strength
360:
354:
335:
332:
282:
281:
279:
278:
271:
264:
256:
253:
252:
251:
250:
245:
240:
235:
230:
225:
220:
215:
210:
205:
200:
195:
190:
185:
180:
175:
170:
162:
161:
145:
144:
127:September 2010
59:
57:
50:
26:
24:
14:
13:
10:
9:
6:
4:
3:
2:
3204:
3193:
3190:
3188:
3185:
3183:
3180:
3178:
3175:
3173:
3172:Glass physics
3170:
3168:
3165:
3163:
3160:
3158:
3155:
3154:
3152:
3137:
3134:
3132:
3129:
3127:
3124:
3123:
3121:
3117:
3109:
3108:
3104:
3103:
3102:
3099:
3097:
3094:
3090:
3089:
3085:
3084:
3083:
3080:
3076:
3075:
3071:
3070:
3069:
3066:
3064:
3061:
3059:
3056:
3054:
3053:Ernst Haeckel
3051:
3049:
3048:Adolf Zeising
3046:
3042:
3041:
3037:
3036:
3035:
3032:
3030:
3027:
3025:
3022:
3020:
3017:
3016:
3014:
3010:
3002:
2999:
2997:
2994:
2992:
2989:
2987:
2984:
2983:
2982:
2979:
2975:
2972:
2970:
2967:
2965:
2962:
2961:
2960:
2957:
2953:
2950:
2948:
2945:
2943:
2940:
2938:
2935:
2934:
2933:
2930:
2928:
2925:
2924:
2922:
2918:
2913:
2903:
2900:
2898:
2895:
2893:
2892:Vortex street
2890:
2888:
2885:
2881:
2878:
2876:
2873:
2871:
2870:Quasicrystals
2868:
2866:
2863:
2862:
2861:
2858:
2856:
2853:
2851:
2848:
2846:
2843:
2841:
2838:
2836:
2833:
2831:
2828:
2826:
2823:
2822:
2820:
2816:
2812:
2805:
2800:
2798:
2793:
2791:
2786:
2785:
2782:
2770:
2767:
2765:
2762:
2760:
2757:
2755:
2752:
2750:
2747:
2745:
2742:
2740:
2737:
2735:
2732:
2731:
2729:
2725:
2719:
2718:Thermal shock
2716:
2714:
2711:
2709:
2706:
2704:
2701:
2700:
2698:
2694:
2688:
2685:
2683:
2680:
2678:
2675:
2673:
2670:
2668:
2665:
2664:
2662:
2658:
2654:
2647:
2642:
2640:
2635:
2633:
2628:
2627:
2624:
2618:
2615:
2613:
2610:
2608:
2604:
2601:
2600:
2596:
2591:
2587:
2585:
2584:0-471-13576-3
2581:
2578:
2574:
2571:
2569:
2568:0-07-100406-8
2565:
2562:
2558:
2557:
2553:
2544:
2538:
2530:
2526:
2522:
2516:
2512:
2511:
2503:
2501:
2499:
2497:
2493:
2489:
2482:
2479:
2474:
2470:
2466:
2462:
2458:
2454:
2450:
2443:
2440:
2435:
2433:1-57766-425-6
2429:
2425:
2418:
2416:
2414:
2410:
2406:
2401:
2398:
2393:
2387:
2379:
2375:
2371:
2365:
2361:
2354:
2351:
2346:
2342:
2338:
2336:0-7131-3515-8
2332:
2328:
2327:
2319:
2317:
2315:
2313:
2309:
2304:
2300:
2296:
2290:
2286:
2279:
2276:
2271:
2265:
2261:
2254:
2251:
2246:
2242:
2238:
2234:
2230:
2226:
2222:
2218:
2211:
2208:
2203:
2199:
2192:
2185:
2182:
2177:
2171:
2167:
2160:
2158:
2156:
2154:
2152:
2150:
2148:
2144:
2139:
2133:
2125:
2119:
2115:
2108:
2106:
2104:
2102:
2100:
2098:
2096:
2094:
2092:
2088:
2084:
2079:
2073:
2069:
2064:
2059:
2055:
2051:
2047:
2040:
2038:
2034:
2030:
2023:
2020:
2015:
2013:0-471-65653-4
2009:
2005:
1998:
1996:
1992:
1988:
1981:
1978:
1971:
1963:
1957:
1954:
1948:
1945:
1938:
1933:
1930:
1928:
1925:
1923:
1920:
1918:
1915:
1913:
1910:
1908:
1905:
1903:
1900:
1898:
1895:
1893:
1890:
1888:
1885:
1883:
1880:
1878:
1875:
1873:
1870:
1868:
1865:
1864:
1859:
1854:
1851:
1848:
1845:
1844:
1843:
1840:
1833:
1831:
1809:
1807:
1801:
1795:
1791:
1787:
1780:
1775:
1771:
1770:Liberty ships
1767:
1763:
1760:
1756:
1755:Silver Bridge
1752:
1748:
1745:
1741:
1740:
1739:
1732:
1730:
1724:Fiber bundles
1723:
1721:
1719:
1715:
1711:
1707:
1667:
1665:
1630:
1576:. This value
1528:
1527:fatigue crack
1524:
1495:
1413:
1390:
1382:
1359:
1338:
1337:
1336:
1311:
1287:
1274:
1270:
1251:
1250:
1249:
1246:
1244:
1240:
1201:
1199:
1195:
1188:
1186:
1182:
1180:
1176:
1175:transgranular
1172:
1167:
1159:
1155:
1153:
1149:
1145:
1136:
1129:
1127:
1123:
1117:
1111:
1109:
1104:
1090:
1070:
1047:
1038:
1034:
1030:
1027:
1022:
1019:
1016:
1009:
977:
969:
968:
967:
949:
942:
927:
920:
879:
871:
870:
869:
848:
845:
813:
809:
806:
802:
795:
792:
786:
783:
780:
776:
746:
742:
686:
678:
677:
676:
656:
652:
644:
641:
625:
618:
615:
599:
588:
584:
583:
582:
560:
556:
551:
548:
541:
500:
492:
491:
490:
488:
483:
481:
477:
473:
469:
468:
462:
459:
455:
447:
442:
434:
427:
425:
423:
415:
413:
410:
406:
400:
398:
393:
391:
387:
383:
372:
369:
366:
364:
361:
359:
356:
355:
351:
345:
341:
333:
331:
329:
324:
320:
316:
314:
313:
308:
304:
300:
296:
292:
288:
277:
272:
270:
265:
263:
258:
257:
255:
254:
249:
246:
244:
241:
239:
238:Thermal shock
236:
234:
231:
229:
226:
224:
221:
219:
216:
214:
211:
209:
206:
204:
201:
199:
196:
194:
191:
189:
186:
184:
181:
179:
176:
174:
171:
169:
166:
165:
164:
163:
158:
151:
141:
138:
130:
119:
116:
112:
109:
105:
102:
98:
95:
91:
88: –
87:
83:
82:Find sources:
76:
72:
66:
65:
60:This article
58:
54:
49:
48:
45:
41:
37:
36:Bone fracture
33:
19:
3105:
3086:
3072:
3038:
2964:Chaos theory
2887:Tessellation
2824:
2743:
2589:
2576:
2560:
2509:
2487:
2481:
2456:
2452:
2442:
2423:
2400:
2359:
2353:
2325:
2284:
2278:
2259:
2253:
2223:(3): 36009.
2220:
2216:
2210:
2201:
2197:
2184:
2165:
2113:
2053:
2049:
2028:
2022:
2003:
1986:
1980:
1956:
1947:
1892:Fractography
1841:
1837:
1813:
1805:
1788:
1784:
1736:
1727:
1706:demonstrated
1671:
1631:
1438:
1334:
1247:
1205:
1196:
1192:
1183:
1168:
1164:
1141:
1124:
1112:
1105:
1062:
965:
867:
674:
580:
484:
465:
463:
451:
419:
401:
394:
386:tensile test
379:
317:
310:
306:
302:
298:
297:or simply a
294:
286:
285:
197:
133:
124:
114:
107:
100:
93:
81:
69:Please help
64:verification
61:
44:
3082:Alan Turing
3040:Liber Abaci
2959:Mathematics
2865:in crystals
2855:Soap bubble
2850:Phyllotaxis
2672:Carbonation
1759:Hoan Bridge
1179:dislocation
344:Venus Prime
312:dislocation
303:shear crack
3151:Categories
3029:Empedocles
3024:Pythagoras
2942:Camouflage
2880:in biology
2875:in flowers
2845:Parastichy
2708:Haloclasty
2677:Hydrolysis
2667:Biological
2204:: 219–230.
2123:0803120826
1972:References
1738:fracture:
1496:of length
97:newspapers
86:"Fracture"
3182:Mechanics
3131:Emergence
3034:Fibonacci
2769:Taphonomy
2754:Saprolite
2739:Etchplain
2687:Oxidation
2537:cite book
2529:908077872
2473:0001-6160
2386:cite book
2378:903959750
2303:992798630
2132:cite book
2072:2424-9424
1768:in 1912,
1749:Bridges:
1733:Disasters
1541:′
1508:′
1391:σ
1288:π
1275:σ
1071:ρ
1023:ρ
1020:γ
978:σ
950:ρ
880:σ
849:ρ
814:σ
796:ρ
747:σ
687:σ
626:γ
581:where: –
552:γ
501:σ
489:in 1921:
446:crank arm
307:slip band
173:Corrosion
2860:Symmetry
2818:Patterns
2744:Fracture
2345:14377078
1860:See also
1241:and the
467:cleavage
370:Fracture
334:Strength
287:Fracture
248:Yielding
198:Fracture
168:Buckling
3119:Related
2986:Crystal
2981:Physics
2969:Fractal
2947:Mimicry
2932:Biology
2840:Meander
2734:Erosion
2245:5975098
2225:Bibcode
1932:Crazing
1776:in 1943
1766:Titanic
1764:Ships:
1761:in 2000
1335:Where:
1202:Testing
1148:necking
1144:ductile
1130:Ductile
868:where:
638:is the
612:is the
454:brittle
428:Brittle
193:Fouling
188:Fatigue
111:scholar
3012:People
2920:Causes
2582:
2566:
2527:
2517:
2471:
2430:
2376:
2366:
2343:
2333:
2301:
2291:
2266:
2243:
2172:
2120:
2070:
2010:
1350:
1302:
1245:test.
722:
291:stress
208:Impact
113:
106:
99:
92:
84:
3019:Plato
2825:Crack
2241:S2CID
2194:(PDF)
1939:Notes
1714:Evans
1710:Faber
1523:notch
1494:notch
642:, and
416:Types
382:fails
309:, or
299:crack
183:Creep
118:JSTOR
104:books
2897:Wave
2835:Foam
2830:Dune
2749:Rock
2580:ISBN
2564:ISBN
2543:link
2525:OCLC
2515:ISBN
2469:ISSN
2428:ISBN
2392:link
2374:OCLC
2364:ISBN
2341:OCLC
2331:ISBN
2299:OCLC
2289:ISBN
2264:ISBN
2170:ISBN
2138:link
2118:ISBN
2068:ISSN
2008:ISBN
1962:jack
1712:and
243:Wear
90:news
2461:doi
2233:doi
2058:doi
1708:by
1554:to
1142:In
452:In
73:by
3153::
2539:}}
2535:{{
2523:.
2495:^
2467:.
2457:31
2455:.
2451:.
2412:^
2388:}}
2384:{{
2372:.
2339:.
2311:^
2297:.
2239:.
2231:.
2221:96
2219:.
2202:55
2200:.
2196:.
2146:^
2134:}}
2130:{{
2090:^
2066:.
2054:01
2052:.
2048:.
2036:^
1994:^
1629:.
1118:(K
330:.
315:.
305:,
2803:e
2796:t
2789:v
2645:e
2638:t
2631:v
2592:.
2545:)
2531:.
2475:.
2463::
2436:.
2394:)
2380:.
2347:.
2305:.
2272:.
2247:.
2235::
2227::
2178:.
2140:)
2126:.
2085:.
2074:.
2060::
2016:.
1828:T
1824:u
1820:T
1816:u
1689:c
1683:K
1649:c
1643:K
1614:c
1608:K
1585:c
1563:c
1538:c
1505:c
1479:c
1455:c
1449:K
1422:c
1396:F
1367:)
1364:a
1360:/
1356:c
1353:(
1347:f
1319:)
1316:a
1312:/
1308:c
1305:(
1299:f
1292:c
1280:F
1271:=
1265:c
1261:K
1222:c
1216:K
1120:c
1091:a
1048:.
1039:o
1035:r
1031:a
1028:4
1017:E
1010:=
1004:e
1001:r
998:u
995:t
992:c
989:a
986:r
983:f
928:a
903:d
900:e
897:i
894:l
891:p
888:p
885:a
846:a
837:d
834:e
831:i
828:l
825:p
822:p
819:a
810:2
807:=
803:)
793:a
787:2
784:+
781:1
777:(
770:d
767:e
764:i
761:l
758:p
755:p
752:a
743:=
737:k
734:c
731:a
728:r
725:c
719:l
716:a
713:c
710:i
707:t
704:p
701:i
698:l
695:l
692:e
657:o
653:r
600:E
561:o
557:r
549:E
542:=
536:l
533:a
530:c
527:i
524:t
521:e
518:r
515:o
512:e
509:h
506:t
346:.
275:e
268:t
261:v
140:)
134:(
129:)
125:(
115:·
108:·
101:·
94:·
67:.
42:.
20:)
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
