1174:
389:
373:
in steels can decrease toughness dramatically. Phosphorus can segregate on grain boundary and lead to intergranular fracture. If the dephosphorization is improved during steelmaking, the steel will be toughened for a lower phosphorus content. After appropriate processing of steel, crystalline grains and second phases that are oriented along rolling direction can improve toughness of materials by delamination which can relax triaxial stress and blunt the crack tip.
2023:
780:
transformation is lower than room temperature. The stress field near the crack tip triggers the martensitic transformation at velocities hypothesized to approach that of sound in the material. The martensitic transformation causes volume expansion (volumetric/ dilatational strain) and shear strains of about 4% and 16% respectively. It applies compressive stress at the crack tip to prevent crack propagation as well as closure
772:
22:
361:
and can be transformed to martensite during deformation. The work associated to phase transformation contributes to the improvement of toughness. In a monolithic Pd–Ag–P–Si–Ge glass alloy, the properties of high bulk modulus and low shear modulus lead to proliferation of shear bands. These bands are self constrained and the toughness is improved.
2183:
microcracks form around elastomeric dispersion above or below the fracture plane. The HIPS is toughened by additional work associated with formation of microcracks. In epoxies, glass particles are used to improve toughness of materials. The toughening mechanism is similar with crack deflection. The addition of
352:
some safety-critical structural part such as pressure vessels and pipelines to aluminum alloy air frames are manufactured in relatively low strength version. Nonetheless, toughness should be improved without sacrificing its strength in metal. Designing a new alloy or improving its processing can achieve this goal.
2182:
Toughening mechanisms in polymers are similar with that have been discussed above. There are only several examples are used to explain the toughening in polymers. In high-impact polystyrene (HIPS), the elastomeric dispersion is used to improve crack propagation resistance. When main crack propagates,
360:
matrix and show an adverse effect on toughness. In 18%Ni-maraging steel, the carbon content is lower and martensite is strengthened by substitutional Ni atoms. In addition, transformation induced plasticity (TRIP) effects in steel can provide additional toughness. In TRIP steel, matrix is metastable
372:
particles lead to easy crack nucleation and fast crack propagation within the planar slip bands. Therefore, toughness of titanium alloy is decreased. Multiple vacuum arc melting (VAR) technique can be used to minimize the oxygen content and increase the toughness of the alloy. Similarly, phosphorus
1186:
In metal matrix composites (MMCs), the additions strengthen the metal and reduce the toughness of material. In ceramic matrix composites (CMCs), the additions can toughen materials but not strengthen them. at same time. In carbon fiber reinforced composites (CFRPs), graphite fibers can toughen and
973:
is the fraction of tetragonal grains that is related to microcracks in an affected volume. The tetragonal particle size should be controlled properly. It is due to that too large particle size leads to spontaneous transformation and too small particle size leads to a very small toughening effect.
754:
is the fraction of grains that is related to microcracks in an affected volume. In this equation, it has been assumed that residual stress is dominant in nucleating microcracks and formation of microcracks is caused by elastic work. In order to retard crack propagation, these microcracks must form
505:
Microcrack toughening means that the formation of microcracks before the main crack can toughen the ceramic. Additional microcracks will cause stress to concentrate in front of the main crack. This leads to additional irreversible work required for crack propagation. In addition, these microcracks
1169:
may also serve to toughen ceramics through crack deflection mechanisms. Formation of a textured internal structure within ceramics can be used as a toughening approach. silicon carbide materials have toughened by this approach. Because the interfacial surface area is increased due to the internal
409:
is the grain boundary energy. Though the irreversible work is decreased because of grain boundary energy, the fracture area is increased in intergranular crack propagation. Moreover, Mode II crack can be caused by deflection from normal fracture plane during intergranular crack propagation, which
351:
In a low yield strength material, the crack tip can be blunted easily and larger crack tip radius is formed. Thus, in a given metallic alloy, toughness in a low-strength condition is usually higher than for higher strength conditions because less plasticity is available for toughening. Therefore,
384:
Ceramics are more brittle than most metals and plastics. The irreversible work associated with plastic deformation is not presented in ceramics. Hence, the methods that improve the toughness of ceramics are different from metals. There are several toughening mechanisms called crack deflection,
126:
refers to the process of making a material more resistant to the propagation of cracks. When a crack propagates, the associated irreversible work in different materials classes is different. Thus, the most effective toughening mechanisms differ among different materials classes. The crack tip
779:
The TRIP effect is found in partially stabilized zirconia. Partially stabilized zirconia is composed of tetragonal phase at high temperature and monoclinic phase and cubic phase at lower temperature in equilibrium. In some components, the onset temperature of tetragonal monoclinic martensite
982:
When a crack propagates in an irregular path, some grains of each side of main crack may protrude into other side. This leads to additional work for a complete fracture. This irreversible work is related to residual stress, which is about . The increment of toughness can be expressed by:
2018:
1421:
is the additional toughness caused by bridging toughening. After crack propagates across through fiber, the fiber is elongated and is pulled out from matrix. These processes correspond to plastic deformation and pull-out work and contribute to toughening of composite.
1849:
is the debond length. From the equation, it can be found that higher flow stress and longer debond length can improve the toughening. However, longer debond length usually lead to a decrease of flow stress because of loss of constraint for plastic deformation.
755:
during crack propagation. The grain size should be smaller than a critical grain size to avoid spontaneous formation of microcracks. The distance between microcrack and fracture plane should be larger than grain size to have a toughening effect. As
1880:
by linear superposition of the matrix and crack bridging based on solutions by Tada. This model can predict behavior for small-scale bridging (bridge length << crack length) under monotonic loading conditions, but not large scale bridging.
1157:, or AGG, can be harnessed to impart a crack bridging microstructure within a single phase ceramic material. The presence of abnormally long grains serves to bridge crack-wakes and hinders their opening. This has been demonstrated in
496:
form materials that can be considered as “in-situ composites” or “self-reinforced materials. Crack deflections around second phase particles have also been used in fracture mechanics approaches to predict fracture toughness increases.
1515:
784:
at the crack wake. From another point of view, the work associated to this phase transformation contributes to the improvement of toughness. The increment of toughness caused by transformation toughening can be expressed by:
623:
355:
Designing a new alloy can be explained by different toughness in several ferrous alloy.18%Ni-maraging steel has a higher toughness than the martensitic steel AISI 4340. In an AISI 4340 alloy, interstitial carbon exist in a
2744:
Nagasawa, Toshio; Kohtoku, Yasuhiko; Hogami, Toshihiko; Matsunaga, Kenji; Kajii, Shinji; Ishikawa, Toshihiro (1998-11-13). "A Tough, Thermally
Conductive Silicon Carbide Composite with High Strength up to 1600°C in Air".
2796:
Johnson, William L.; Demetriou, Marios D.; Lind, Mary-Laura; Duan, Gang; Wiest, Aaron; Suh, Jin-Yoo; Hofmann, Douglas C. (2008). "Designing metallic glass matrix composites with high toughness and tensile ductility".
861:
1052:
211:
1717:
410:
furtherly improves the toughness of ceramics. As a result, the ceramics with intergranular fracture shows a higher toughness than that with transgranular fracture. In SiC, the fracture toughness is ~2-3
1886:
1279:
763:
in 1981, the toughening induced by the incorporation of second-phase particles subject to microcracking becomes appreciable for a narrow size distribution of particles of appropriate size.
143:
material such as a metal, this toughness is typically proportional to the fracture stress and strain as well as the gauge length of the crack. The plane strain toughness in a metal is given by:
1641:
When fiber is ductile, the work from plastic deformation mainly contributes to the improvement of toughens. The additional toughness contributed by plastic deformation can be expressed by:
2973:
Zeidi, Mahdi; Kim, Chun IL; Park, Chul B. (2021). "The role of interface on the toughening and failure mechanisms of thermoplastic nanocomposites reinforced with nanofibrillated rubbers".
1633:
is the interface friction stress. From the equation, it can be found that higher volume fraction, higher fiber strength and lower interfacial stress can get a better toughening effect.
376:
Metals can also be strengthened by the methods described below for ceramics, but these methods generally have a lesser impact on toughening than plasticity induced crack blunting.
2283:
Ritchie, Robert O.; Johnson, William L.; Hofmann, Douglas C.; Schramm, Joseph P.; Garrett, Glenn; Launey, Maximilien E.; Demetriou, Marios D. (2011). "A damage-tolerant glass".
246:
486:
447:
1425:
When fiber is brittle, the pull-out work dominates the irreversible work contributing to toughening. The increment of toughness caused by pull-out work can be expressed by:
702:
326:
1793:
944:
2085:
1419:
296:
2152:
1766:
1564:
1101:
917:
679:
725:
506:
can cause crack branches, and one crack can form multiple cracks. Because of the formation of these cracks, irreversible work is increased. The increment of toughness
2172:
1537:
364:
Metals can be toughened by improvement of processing. With a high affinity for oxygen, titanium alloy can absorb oxygen easily. Oxygen can promote the formation of α
2055:
1878:
1847:
1820:
1631:
1611:
1389:
1362:
1335:
1308:
1148:
971:
890:
752:
652:
531:
346:
1074:
2435:
Tsuzaki, Kaneaki; Yin, Fuxing; Inoue, Tadanobu; Kimura, Yuuji (2008-05-23). "Inverse
Temperature Dependence of Toughness in an Ultrafine Grain-Structure Steel".
2125:
2105:
1739:
1584:
1187:
strengthen polymer at same time. In bulk metallic glass composites(BMGs), dendrites are added to hind the movement of shear band and the toughness is improved.
1121:
266:
2494:
Gilbert, C. J.; Cao, J. J.; Jonghe, L. C. de; Ritchie, R. O. (1997). "Crack-Growth
Resistance-Curve Behavior in Silicon Carbide: Small versus Long Cracks".
1430:
538:
1190:
If fibers have larger fracture strain than matrix, the composite is toughened by crack bridging. The toughness of a composite can be expressed:
2630:
790:
988:
149:
1646:
2902:
2867:
2665:
401:
In polycrystalline ceramics, the crack can propagate in an intergranular way. The associated irreversible work per unit area is 2Îł-Îł
105:
2013:{\displaystyle K_{c}=K_{m}+\Delta K_{b}=K_{m}+{\sqrt {\frac {2}{\pi }}}\alpha V_{f}\int _{0}^{L}{\frac {\sigma _{y}}{\sqrt {x}}}dx}
1195:
43:
2528:
86:
58:
3030:
488:
when it fractures intergranularly. Crack deflection mechanisms bring about increased toughness in ceramics exhibiting
39:
2400:
Bandyopadhyay, N.; Briant, C. L. (1982). "The Effect of
Phosphorus on Intergranular Caustic Cracking of NiCr Steel".
2334:
Neuberger, B. W.; Oberson, P. G.; Ankem, S. (2011-05-01). "The Effect of
Yttrium on Ti-5111 Gas Tungsten Arc Welds".
65:
32:
1153:
There are some other approaches to improve the toughness of ceramics through crack bridging. The phenomenon of
1853:
The toughness in a composite with ductile phase toughening can also be shown using stress intensity factor,
72:
1173:
2581:
1166:
1154:
493:
489:
219:
54:
452:
413:
2939:
2806:
2754:
2444:
2343:
2292:
2241:
781:
357:
684:
301:
2022:
1771:
922:
2060:
1394:
388:
271:
3006:
2838:
2726:
2476:
2367:
2130:
1744:
1542:
1079:
895:
657:
2529:
Effect of Grain Growth of B-Silicon
Nitride on Strength, Weibull Modulus, and Fracture Toughness
2688:
2998:
2990:
2955:
2908:
2898:
2873:
2863:
2830:
2822:
2778:
2770:
2718:
2671:
2661:
2636:
2626:
2601:
2562:
2511:
2468:
2460:
2417:
2359:
2316:
2308:
2265:
2257:
756:
707:
119:
2222:
Courtney, T. H. (2005). Mechanical
Behavior of Materials. United States: Waveland Press, Inc.
2157:
2982:
2947:
2814:
2762:
2710:
2593:
2554:
2503:
2452:
2409:
2351:
2300:
2249:
1522:
2033:
1856:
1825:
1798:
1616:
1589:
1367:
1340:
1313:
1286:
1126:
949:
868:
771:
730:
630:
509:
331:
2928:"Small-scale crack bridging and the fracture toughness of particulate-reinforced ceramics"
1162:
1158:
1059:
760:
131:
have limited crack tip plasticity and primarily rely on different toughening mechanisms.
2943:
2810:
2758:
2448:
2347:
2296:
2245:
79:
2597:
2507:
2110:
2090:
1724:
1569:
1106:
251:
2951:
2542:
1510:{\displaystyle \Delta G_{C}={1 \over 32}{\beta ^{2}\sigma _{f}^{2}V_{f}d \over \tau }}
3024:
3010:
2842:
2730:
2558:
2371:
2927:
2480:
2184:
2766:
2714:
618:{\displaystyle \Delta G_{C}\cong 2r_{c}\sigma _{R}(\Delta \alpha )(\Delta T)V_{f}}
21:
2640:
2355:
2994:
2959:
2912:
2826:
2774:
2722:
2675:
2605:
2566:
2515:
2464:
2421:
2363:
2312:
2261:
704:
is the difference of thermal expansion coefficient between adjacent grains,
449:
if it fractures transgranularly and the fracture toughness is improved to 10
2877:
2456:
892:
is the distance between boundary of transformed region with fracture plane,
3002:
2834:
2620:
2472:
2320:
2269:
2232:
Ritchie, Robert O. (2011). "The conflicts between strength and toughness".
2782:
1170:
structure, the irreversible fracture work is increased in this material.
2857:
2188:
127:
plasticity is important in toughening of metals and long-chain polymers.
2818:
2986:
775:
Schematic of transformation toughening in partially stabilized zirconia
140:
128:
2413:
385:
microcrack toughening, transformation toughening, and crack bridging.
2892:
2655:
2304:
2253:
856:{\displaystyle \Delta G_{C}\cong 2r_{c}\sigma _{M}\epsilon _{M}V_{f}}
1047:{\displaystyle \Delta G_{C}\cong {1 \over 8}\mu \sigma _{R}V_{f}d}
387:
206:{\displaystyle G_{\mathrm {I} C}=B\sigma _{yf}\epsilon _{fr}\rho }
2926:
Budiansky, Bernard; Amazigo, John C.; Evans, Anthony G. (1988).
1712:{\displaystyle \Delta G_{C}=C\sigma _{y}\epsilon _{f}V_{f}l_{d}}
15:
2654:
Soboyejo, Wole O. (2003). "13.4 Transformation toughening".
2856:
Tada, Hiroshi; Paris, P. C.; Irwin, George Rankin (2000).
2691:
in
Journal of Crystal Growth 2012, Volume 359, Pages 83-91
1150:
is the fraction of grains associated with crack bridging.
727:
is the temperature difference causing thermal strain, and
2582:"Toughening of Ceramics by Circumferential Microcracking"
1539:
is the ratio between debond length and critical length,
2701:
Tredway, William K. (1998-11-13). "Toughened
Ceramics".
1274:{\displaystyle G_{C}=V_{m}G_{m}+V_{f}G_{f}+\Delta G_{C}}
654:
is the distance between microcracks and fracture plane,
2160:
2133:
2113:
2093:
2063:
2036:
1889:
1859:
1828:
1801:
1774:
1747:
1727:
1649:
1619:
1592:
1572:
1545:
1525:
1433:
1397:
1370:
1343:
1316:
1289:
1198:
1129:
1109:
1082:
1062:
991:
952:
925:
919:
is the stress triggering martensite transformation,
898:
871:
793:
733:
710:
687:
660:
633:
541:
512:
492:(AGG). The heterogeneous microstructures produced by
455:
416:
334:
304:
274:
254:
222:
152:
46:. Unsourced material may be challenged and removed.
2166:
2146:
2119:
2099:
2079:
2049:
2012:
1872:
1841:
1814:
1787:
1760:
1733:
1711:
1625:
1605:
1578:
1558:
1531:
1509:
1413:
1383:
1356:
1329:
1302:
1273:
1142:
1115:
1095:
1068:
1046:
965:
938:
911:
884:
855:
746:
719:
696:
673:
646:
617:
533:due to microcrack toughening can be expressed by:
525:
480:
441:
340:
320:
290:
268:is a constant that incorporates the stress state,
260:
240:
205:
2891:Soboyejo, Wole O. (2003). "13.5 Crack Bridging".
1337:are toughness of matrix and fibers respectively,
946:is the strain of martensite transformation, and
405:, where Îł is the surface energy of material and Îł
2932:Journal of the Mechanics and Physics of Solids
1391:are volume of matrix and fibers respectively,
2894:Mechanical properties of engineered materials
2657:Mechanical properties of engineered materials
2387:Engineering materials and processes: titanium
2191:is also a good way to improve its toughness.
8:
2385:LĂĽtjering, Gerd; Williams, James C (2007).
2336:Metallurgical and Materials Transactions A
2541:Faber, K. T.; Evans, A. G. (1983-04-01).
2159:
2138:
2132:
2112:
2092:
2087:is the toughening due to crack bridging,
2071:
2062:
2057:is the fracture toughness of the matrix,
2041:
2035:
1991:
1985:
1979:
1974:
1964:
1945:
1936:
1923:
1907:
1894:
1888:
1864:
1858:
1833:
1827:
1806:
1800:
1779:
1773:
1752:
1746:
1726:
1703:
1693:
1683:
1673:
1657:
1648:
1618:
1597:
1591:
1571:
1550:
1544:
1524:
1492:
1482:
1477:
1467:
1460:
1450:
1441:
1432:
1405:
1396:
1375:
1369:
1348:
1342:
1321:
1315:
1294:
1288:
1265:
1249:
1239:
1226:
1216:
1203:
1197:
1134:
1128:
1108:
1087:
1081:
1061:
1035:
1025:
1008:
999:
990:
957:
951:
930:
924:
903:
897:
876:
870:
847:
837:
827:
817:
801:
792:
738:
732:
709:
686:
665:
659:
638:
632:
609:
575:
565:
549:
540:
517:
511:
472:
454:
433:
415:
333:
309:
303:
279:
273:
253:
228:
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221:
191:
178:
158:
157:
151:
106:Learn how and when to remove this message
2531:Journal of the American Ceramic Society
2021:
1172:
770:
298:is the tensile flow stress at fracture,
2586:Journal of the American Ceramic Society
2496:Journal of the American Ceramic Society
2200:
2026:Several toughening mechanism in epoxies
2862:(3rd ed.). New York: ASME Press.
2859:The stress analysis of cracks handbook
2543:"Crack deflection processes—I. Theory"
2127:is the distance behind the crack tip,
2622:Transformation Toughening Of Ceramics
2174:is a constraint/ triaxiality factor.
1177:Schematic fiber-reinforced composites
7:
2218:
2216:
2214:
2212:
2210:
2208:
2206:
2204:
328:is the tensile fracture strain, and
44:adding citations to reliable sources
2580:Evans, A. G.; Faber, K. T. (1981).
2598:10.1111/j.1151-2916.1981.tb09877.x
2508:10.1111/j.1151-2916.1997.tb03115.x
2389:. New York: Springer. p. 221.
2154:is the uniaxial yield stress, and
2064:
1916:
1795:is the fracture strain of fibers,
1650:
1434:
1398:
1258:
992:
794:
711:
688:
596:
584:
542:
229:
159:
14:
2625:. Milton: CRC Press. p. 14.
1123:is the edge length of grain, and
241:{\displaystyle G_{\mathrm {I} C}}
1076:is the coefficient of friction,
481:{\displaystyle MPa\cdot m^{0.5}}
442:{\displaystyle MPa\cdot m^{0.5}}
20:
1822:is the fraction of fibers, and
1768:is the flow stress of fibers,
248:is the plane strain toughness,
31:needs additional citations for
1741:is a constant between 1.5-6,
1613:is the fraction of fibers and
697:{\displaystyle \Delta \alpha }
602:
593:
590:
581:
321:{\displaystyle \epsilon _{fr}}
1:
2952:10.1016/s0022-5096(98)90003-5
2767:10.1126/science.282.5392.1295
2715:10.1126/science.282.5392.1275
1788:{\displaystyle \epsilon _{y}}
939:{\displaystyle \epsilon _{M}}
2559:10.1016/0001-6160(83)90046-9
2080:{\displaystyle \Delta K_{b}}
1637:Ductile phase crack bridging
1414:{\displaystyle \Delta G_{C}}
392:Common toughening mechanisms
348:is the radius of crack tip.
291:{\displaystyle \sigma _{yf}}
2147:{\displaystyle \sigma _{y}}
1761:{\displaystyle \sigma _{y}}
1566:is the strength of fibers,
1559:{\displaystyle \sigma _{f}}
1096:{\displaystyle \sigma _{R}}
912:{\displaystyle \sigma _{M}}
674:{\displaystyle \sigma _{R}}
3047:
2356:10.1007/s11661-010-0532-8
767:Transformation toughening
358:bcc (body centered cubic)
2619:Green, David J. (2018).
1182:Toughening in composites
720:{\displaystyle \Delta T}
2457:10.1126/science.1156084
2167:{\displaystyle \alpha }
1586:is the width of fiber,
1167:Abnormally large grains
368:phase. These coherent α
2178:Toughening in polymers
2168:
2148:
2121:
2107:is the bridge length,
2101:
2081:
2051:
2027:
2014:
1874:
1843:
1816:
1789:
1762:
1735:
1713:
1627:
1607:
1580:
1560:
1533:
1532:{\displaystyle \beta }
1511:
1415:
1385:
1358:
1331:
1304:
1275:
1178:
1144:
1117:
1097:
1070:
1048:
967:
940:
913:
886:
857:
776:
748:
721:
698:
675:
648:
619:
527:
482:
443:
393:
380:Toughening in ceramics
342:
322:
292:
262:
242:
207:
2689:Abnormal Grain Growth
2169:
2149:
2122:
2102:
2082:
2052:
2050:{\displaystyle K_{m}}
2025:
2015:
1875:
1873:{\displaystyle K_{c}}
1844:
1842:{\displaystyle l_{d}}
1817:
1815:{\displaystyle V_{f}}
1790:
1763:
1736:
1714:
1628:
1626:{\displaystyle \tau }
1608:
1606:{\displaystyle V_{f}}
1581:
1561:
1534:
1512:
1416:
1386:
1384:{\displaystyle V_{f}}
1359:
1357:{\displaystyle V_{m}}
1332:
1330:{\displaystyle G_{f}}
1305:
1303:{\displaystyle G_{m}}
1276:
1176:
1155:abnormal grain growth
1145:
1143:{\displaystyle V_{f}}
1118:
1103:is residual stress,
1098:
1071:
1049:
968:
966:{\displaystyle V_{f}}
941:
914:
887:
885:{\displaystyle r_{c}}
858:
774:
749:
747:{\displaystyle V_{f}}
722:
699:
676:
649:
647:{\displaystyle r_{c}}
620:
528:
526:{\displaystyle G_{C}}
501:Microcrack toughening
490:abnormal grain growth
483:
444:
391:
343:
341:{\displaystyle \rho }
323:
293:
263:
243:
208:
2158:
2131:
2111:
2091:
2061:
2034:
1887:
1857:
1826:
1799:
1772:
1745:
1725:
1647:
1617:
1590:
1570:
1543:
1523:
1431:
1395:
1368:
1341:
1314:
1287:
1196:
1127:
1107:
1080:
1069:{\displaystyle \mu }
1060:
989:
950:
923:
896:
869:
791:
759:most prominently by
731:
708:
685:
681:is residual stress,
658:
631:
539:
510:
453:
414:
332:
302:
272:
252:
220:
150:
135:Toughening in metals
40:improve this article
2981:(47): 20248–20280.
2944:1988JMPSo..36..167B
2819:10.1038/nature06598
2811:2008Natur.451.1085H
2805:(7182): 1085–1089.
2759:1998Sci...282.1295I
2753:(5392): 1295–1297.
2449:2008Sci...320.1057K
2443:(5879): 1057–1060.
2348:2011MMTA...42.1296N
2297:2011NatMa..10..123D
2246:2011NatMa..10..817R
1984:
1487:
3031:Fracture mechanics
2987:10.1039/D1NR07363J
2164:
2144:
2117:
2097:
2077:
2047:
2028:
2010:
1970:
1870:
1839:
1812:
1785:
1758:
1731:
1709:
1623:
1603:
1576:
1556:
1529:
1507:
1473:
1411:
1381:
1354:
1327:
1300:
1271:
1179:
1140:
1113:
1093:
1066:
1044:
963:
936:
909:
882:
853:
777:
744:
717:
694:
671:
644:
615:
523:
478:
439:
394:
338:
318:
288:
258:
238:
203:
139:For the case of a
2897:. Marcel Dekker.
2660:. Marcel Dekker.
2632:978-1-351-08585-4
2547:Acta Metallurgica
2414:10.5006/1.3579264
2120:{\displaystyle x}
2100:{\displaystyle L}
2002:
2001:
1955:
1954:
1734:{\displaystyle C}
1579:{\displaystyle d}
1505:
1458:
1116:{\displaystyle d}
1016:
261:{\displaystyle B}
120:materials science
116:
115:
108:
90:
3038:
3015:
3014:
2970:
2964:
2963:
2923:
2917:
2916:
2888:
2882:
2881:
2853:
2847:
2846:
2793:
2787:
2786:
2741:
2735:
2734:
2698:
2692:
2686:
2680:
2679:
2651:
2645:
2644:
2616:
2610:
2609:
2577:
2571:
2570:
2538:
2532:
2526:
2520:
2519:
2502:(9): 2253–2261.
2491:
2485:
2484:
2432:
2426:
2425:
2397:
2391:
2390:
2382:
2376:
2375:
2342:(5): 1296–1309.
2331:
2325:
2324:
2305:10.1038/nmat2930
2285:Nature Materials
2280:
2274:
2273:
2254:10.1038/nmat3115
2234:Nature Materials
2229:
2223:
2220:
2173:
2171:
2170:
2165:
2153:
2151:
2150:
2145:
2143:
2142:
2126:
2124:
2123:
2118:
2106:
2104:
2103:
2098:
2086:
2084:
2083:
2078:
2076:
2075:
2056:
2054:
2053:
2048:
2046:
2045:
2019:
2017:
2016:
2011:
2003:
1997:
1996:
1995:
1986:
1983:
1978:
1969:
1968:
1956:
1947:
1946:
1941:
1940:
1928:
1927:
1912:
1911:
1899:
1898:
1879:
1877:
1876:
1871:
1869:
1868:
1848:
1846:
1845:
1840:
1838:
1837:
1821:
1819:
1818:
1813:
1811:
1810:
1794:
1792:
1791:
1786:
1784:
1783:
1767:
1765:
1764:
1759:
1757:
1756:
1740:
1738:
1737:
1732:
1718:
1716:
1715:
1710:
1708:
1707:
1698:
1697:
1688:
1687:
1678:
1677:
1662:
1661:
1632:
1630:
1629:
1624:
1612:
1610:
1609:
1604:
1602:
1601:
1585:
1583:
1582:
1577:
1565:
1563:
1562:
1557:
1555:
1554:
1538:
1536:
1535:
1530:
1516:
1514:
1513:
1508:
1506:
1501:
1497:
1496:
1486:
1481:
1472:
1471:
1461:
1459:
1451:
1446:
1445:
1420:
1418:
1417:
1412:
1410:
1409:
1390:
1388:
1387:
1382:
1380:
1379:
1363:
1361:
1360:
1355:
1353:
1352:
1336:
1334:
1333:
1328:
1326:
1325:
1309:
1307:
1306:
1301:
1299:
1298:
1280:
1278:
1277:
1272:
1270:
1269:
1254:
1253:
1244:
1243:
1231:
1230:
1221:
1220:
1208:
1207:
1149:
1147:
1146:
1141:
1139:
1138:
1122:
1120:
1119:
1114:
1102:
1100:
1099:
1094:
1092:
1091:
1075:
1073:
1072:
1067:
1053:
1051:
1050:
1045:
1040:
1039:
1030:
1029:
1017:
1009:
1004:
1003:
972:
970:
969:
964:
962:
961:
945:
943:
942:
937:
935:
934:
918:
916:
915:
910:
908:
907:
891:
889:
888:
883:
881:
880:
862:
860:
859:
854:
852:
851:
842:
841:
832:
831:
822:
821:
806:
805:
753:
751:
750:
745:
743:
742:
726:
724:
723:
718:
703:
701:
700:
695:
680:
678:
677:
672:
670:
669:
653:
651:
650:
645:
643:
642:
624:
622:
621:
616:
614:
613:
580:
579:
570:
569:
554:
553:
532:
530:
529:
524:
522:
521:
487:
485:
484:
479:
477:
476:
448:
446:
445:
440:
438:
437:
397:Crack deflection
347:
345:
344:
339:
327:
325:
324:
319:
317:
316:
297:
295:
294:
289:
287:
286:
267:
265:
264:
259:
247:
245:
244:
239:
237:
236:
232:
212:
210:
209:
204:
199:
198:
186:
185:
167:
166:
162:
111:
104:
100:
97:
91:
89:
48:
24:
16:
3046:
3045:
3041:
3040:
3039:
3037:
3036:
3035:
3021:
3020:
3019:
3018:
2972:
2971:
2967:
2925:
2924:
2920:
2905:
2890:
2889:
2885:
2870:
2855:
2854:
2850:
2795:
2794:
2790:
2743:
2742:
2738:
2700:
2699:
2695:
2687:
2683:
2668:
2653:
2652:
2648:
2633:
2618:
2617:
2613:
2579:
2578:
2574:
2540:
2539:
2535:
2527:
2523:
2493:
2492:
2488:
2434:
2433:
2429:
2399:
2398:
2394:
2384:
2383:
2379:
2333:
2332:
2328:
2282:
2281:
2277:
2240:(11): 817–822.
2231:
2230:
2226:
2221:
2202:
2197:
2180:
2156:
2155:
2134:
2129:
2128:
2109:
2108:
2089:
2088:
2067:
2059:
2058:
2037:
2032:
2031:
1987:
1960:
1932:
1919:
1903:
1890:
1885:
1884:
1860:
1855:
1854:
1829:
1824:
1823:
1802:
1797:
1796:
1775:
1770:
1769:
1748:
1743:
1742:
1723:
1722:
1699:
1689:
1679:
1669:
1653:
1645:
1644:
1639:
1615:
1614:
1593:
1588:
1587:
1568:
1567:
1546:
1541:
1540:
1521:
1520:
1488:
1463:
1462:
1437:
1429:
1428:
1401:
1393:
1392:
1371:
1366:
1365:
1344:
1339:
1338:
1317:
1312:
1311:
1290:
1285:
1284:
1261:
1245:
1235:
1222:
1212:
1199:
1194:
1193:
1184:
1163:silicon nitride
1159:silicon carbide
1130:
1125:
1124:
1105:
1104:
1083:
1078:
1077:
1058:
1057:
1031:
1021:
995:
987:
986:
980:
953:
948:
947:
926:
921:
920:
899:
894:
893:
872:
867:
866:
843:
833:
823:
813:
797:
789:
788:
769:
761:Katherine Faber
734:
729:
728:
706:
705:
683:
682:
661:
656:
655:
634:
629:
628:
605:
571:
561:
545:
537:
536:
513:
508:
507:
503:
468:
451:
450:
429:
412:
411:
408:
404:
399:
382:
371:
367:
330:
329:
305:
300:
299:
275:
270:
269:
250:
249:
223:
218:
217:
187:
174:
153:
148:
147:
137:
112:
101:
95:
92:
49:
47:
37:
25:
12:
11:
5:
3044:
3042:
3034:
3033:
3023:
3022:
3017:
3016:
2965:
2938:(2): 167–187.
2918:
2903:
2883:
2868:
2848:
2788:
2736:
2709:(5392): 1275.
2693:
2681:
2666:
2646:
2631:
2611:
2592:(7): 394–398.
2572:
2553:(4): 565–576.
2533:
2521:
2486:
2427:
2408:(3): 125–129.
2392:
2377:
2326:
2291:(2): 123–128.
2275:
2224:
2199:
2198:
2196:
2193:
2179:
2176:
2163:
2141:
2137:
2116:
2096:
2074:
2070:
2066:
2044:
2040:
2009:
2006:
2000:
1994:
1990:
1982:
1977:
1973:
1967:
1963:
1959:
1953:
1950:
1944:
1939:
1935:
1931:
1926:
1922:
1918:
1915:
1910:
1906:
1902:
1897:
1893:
1867:
1863:
1836:
1832:
1809:
1805:
1782:
1778:
1755:
1751:
1730:
1706:
1702:
1696:
1692:
1686:
1682:
1676:
1672:
1668:
1665:
1660:
1656:
1652:
1638:
1635:
1622:
1600:
1596:
1575:
1553:
1549:
1528:
1504:
1500:
1495:
1491:
1485:
1480:
1476:
1470:
1466:
1457:
1454:
1449:
1444:
1440:
1436:
1408:
1404:
1400:
1378:
1374:
1351:
1347:
1324:
1320:
1297:
1293:
1268:
1264:
1260:
1257:
1252:
1248:
1242:
1238:
1234:
1229:
1225:
1219:
1215:
1211:
1206:
1202:
1183:
1180:
1137:
1133:
1112:
1090:
1086:
1065:
1043:
1038:
1034:
1028:
1024:
1020:
1015:
1012:
1007:
1002:
998:
994:
979:
978:Crack bridging
976:
960:
956:
933:
929:
906:
902:
879:
875:
850:
846:
840:
836:
830:
826:
820:
816:
812:
809:
804:
800:
796:
768:
765:
741:
737:
716:
713:
693:
690:
668:
664:
641:
637:
612:
608:
604:
601:
598:
595:
592:
589:
586:
583:
578:
574:
568:
564:
560:
557:
552:
548:
544:
520:
516:
502:
499:
475:
471:
467:
464:
461:
458:
436:
432:
428:
425:
422:
419:
406:
402:
398:
395:
381:
378:
369:
365:
337:
315:
312:
308:
285:
282:
278:
257:
235:
231:
226:
214:
213:
202:
197:
194:
190:
184:
181:
177:
173:
170:
165:
161:
156:
136:
133:
114:
113:
28:
26:
19:
13:
10:
9:
6:
4:
3:
2:
3043:
3032:
3029:
3028:
3026:
3012:
3008:
3004:
3000:
2996:
2992:
2988:
2984:
2980:
2976:
2969:
2966:
2961:
2957:
2953:
2949:
2945:
2941:
2937:
2933:
2929:
2922:
2919:
2914:
2910:
2906:
2904:0-8247-8900-8
2900:
2896:
2895:
2887:
2884:
2879:
2875:
2871:
2869:0-7918-0153-5
2865:
2861:
2860:
2852:
2849:
2844:
2840:
2836:
2832:
2828:
2824:
2820:
2816:
2812:
2808:
2804:
2800:
2792:
2789:
2784:
2780:
2776:
2772:
2768:
2764:
2760:
2756:
2752:
2748:
2740:
2737:
2732:
2728:
2724:
2720:
2716:
2712:
2708:
2704:
2697:
2694:
2690:
2685:
2682:
2677:
2673:
2669:
2667:0-8247-8900-8
2663:
2659:
2658:
2650:
2647:
2642:
2638:
2634:
2628:
2624:
2623:
2615:
2612:
2607:
2603:
2599:
2595:
2591:
2587:
2583:
2576:
2573:
2568:
2564:
2560:
2556:
2552:
2548:
2544:
2537:
2534:
2530:
2525:
2522:
2517:
2513:
2509:
2505:
2501:
2497:
2490:
2487:
2482:
2478:
2474:
2470:
2466:
2462:
2458:
2454:
2450:
2446:
2442:
2438:
2431:
2428:
2423:
2419:
2415:
2411:
2407:
2403:
2396:
2393:
2388:
2381:
2378:
2373:
2369:
2365:
2361:
2357:
2353:
2349:
2345:
2341:
2337:
2330:
2327:
2322:
2318:
2314:
2310:
2306:
2302:
2298:
2294:
2290:
2286:
2279:
2276:
2271:
2267:
2263:
2259:
2255:
2251:
2247:
2243:
2239:
2235:
2228:
2225:
2219:
2217:
2215:
2213:
2211:
2209:
2207:
2205:
2201:
2194:
2192:
2190:
2186:
2177:
2175:
2161:
2139:
2135:
2114:
2094:
2072:
2068:
2042:
2038:
2024:
2020:
2007:
2004:
1998:
1992:
1988:
1980:
1975:
1971:
1965:
1961:
1957:
1951:
1948:
1942:
1937:
1933:
1929:
1924:
1920:
1913:
1908:
1904:
1900:
1895:
1891:
1882:
1865:
1861:
1851:
1834:
1830:
1807:
1803:
1780:
1776:
1753:
1749:
1728:
1719:
1704:
1700:
1694:
1690:
1684:
1680:
1674:
1670:
1666:
1663:
1658:
1654:
1642:
1636:
1634:
1620:
1598:
1594:
1573:
1551:
1547:
1526:
1517:
1502:
1498:
1493:
1489:
1483:
1478:
1474:
1468:
1464:
1455:
1452:
1447:
1442:
1438:
1426:
1423:
1406:
1402:
1376:
1372:
1349:
1345:
1322:
1318:
1295:
1291:
1281:
1266:
1262:
1255:
1250:
1246:
1240:
1236:
1232:
1227:
1223:
1217:
1213:
1209:
1204:
1200:
1191:
1188:
1181:
1175:
1171:
1168:
1164:
1160:
1156:
1151:
1135:
1131:
1110:
1088:
1084:
1063:
1054:
1041:
1036:
1032:
1026:
1022:
1018:
1013:
1010:
1005:
1000:
996:
984:
977:
975:
958:
954:
931:
927:
904:
900:
877:
873:
863:
848:
844:
838:
834:
828:
824:
818:
814:
810:
807:
802:
798:
786:
783:
773:
766:
764:
762:
758:
739:
735:
714:
691:
666:
662:
639:
635:
625:
610:
606:
599:
587:
576:
572:
566:
562:
558:
555:
550:
546:
534:
518:
514:
500:
498:
495:
491:
473:
469:
465:
462:
459:
456:
434:
430:
426:
423:
420:
417:
396:
390:
386:
379:
377:
374:
362:
359:
353:
349:
335:
313:
310:
306:
283:
280:
276:
255:
233:
224:
200:
195:
192:
188:
182:
179:
175:
171:
168:
163:
154:
146:
145:
144:
142:
134:
132:
130:
125:
121:
110:
107:
99:
88:
85:
81:
78:
74:
71:
67:
64:
60:
57: –
56:
52:
51:Find sources:
45:
41:
35:
34:
29:This article
27:
23:
18:
17:
2978:
2974:
2968:
2935:
2931:
2921:
2893:
2886:
2858:
2851:
2802:
2798:
2791:
2750:
2746:
2739:
2706:
2702:
2696:
2684:
2656:
2649:
2621:
2614:
2589:
2585:
2575:
2550:
2546:
2536:
2524:
2499:
2495:
2489:
2440:
2436:
2430:
2405:
2401:
2395:
2386:
2380:
2339:
2335:
2329:
2288:
2284:
2278:
2237:
2233:
2227:
2185:plasticizers
2181:
2029:
1883:
1852:
1720:
1643:
1640:
1518:
1427:
1424:
1282:
1192:
1189:
1185:
1152:
1055:
985:
981:
864:
787:
778:
757:demonstrated
626:
535:
504:
400:
383:
375:
363:
354:
350:
215:
138:
123:
117:
102:
93:
83:
76:
69:
62:
55:"Toughening"
50:
38:Please help
33:verification
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