Fishnet Statistical Size Effect on Strength of Materials With Nacreous Microstructure

2019 ◽  
Vol 86 (8) ◽  
Author(s):  
Wen Luo ◽  
Zdeněk P. Bažant
Keyword(s):  
Size Effect ◽  
Failure Probability ◽  
Maximum Load ◽  
Strength Distribution ◽  
Strength Limit ◽  
Nominal Strength ◽  
Geometric Scaling ◽  
Simple Scaling ◽  
Structure Strength ◽  
Architectured Materials

The statistical size effect has generally been explained by the weakest-link model, which is valid if the failure of one representative volume element (RVE) of material, corresponding to one link, suffices to cause failure of the whole structure under the controlled load. As shown by the recent formulation of fishnet statistics, this is not the case for some architectured materials, such as nacre, for which one or several microstructural links must fail before reaching the maximum load or the structure strength limit. Such behavior was shown to bring about major safety advantages. Here, we show that it also alters the size effect on the median nominal strength of geometrically scaled rectangular specimens of a diagonally pulled fishnet. To derive the size effect relation, the geometric scaling of a rectangular fishnet is split into separate transverse and longitudinal scalings, for each of which a simple scaling rule for the median strength is established. Proportional combination of both then yields the two-dimensional geometric scaling and its size effect. Furthermore, a method to infer the material failure probability (or strength) distribution from the median size effect obtained from experiments or Monte Carlo simulations is formulated. Compared to the direct estimation of the histogram, which would require more than ten million test repetitions, the size effect method requires only a few (typically about six) tests for each of three or four structure sizes to obtain a tight upper bound on the failure probability distribution. Finally, comparisons of the model predictions and actual histograms are presented.

scholarly journals Size Effect in Fracture of Sandwich Structure Components: Foam and Laminate

2001 ◽  
Author(s):  
Zdeněk P. Bažant ◽  
Yong Zhou ◽  
Drahomír Novák ◽  
Isaac M. Daniel
Keyword(s):  
Size Effect ◽  
Size Effects ◽  
Sandwich Structure ◽  
Maximum Load ◽  
Material Strength ◽  
Large Structures ◽  
Nominal Strength ◽  
Sandwich Plates And Shells ◽  
Extensive Test ◽  
Plates And Shells

Abstract In the design of sandwich plates and shells for very large structures, such as ships in the range of 100 m length, it is very important to take the size effect on the nominal strength into account, and do so in a realistic, physically justified, manner. Before the size effect is addressed for a sandwich structure, it must be understood for its components — the foam core and the laminate skins. In the current practice, the size effects are automatically attributed to the randomness of material strength, as described by the Weibull theory. The purpose of this paper is to show that in both the foam and the laminate there are deterministic size effects, which are generally more pronounced. They are caused by stress redistribution and energy release due to the growth of large fractures or large cracking zones prior to attaining the maximum load. This deterministic size effect is verified and calibrated by new tests of notched specimens of rigid close-cell vinyl foam. A combined deterministic-probabilistic theory of size effect of the laminates is proposed and verified by extensive test data.

Scaling of Strength of Metal-Composite Joints—Part I: Experimental Investigation

2009 ◽  
Vol 77 (1) ◽  
Author(s):  
Qiang Yu ◽  
Zdeněk P. Bažant ◽  
John Bayldon ◽  
Jia-Liang Le ◽  
Ferhun C. Caner ◽  
...  
Keyword(s):  
Size Effect ◽  
Peak Load ◽  
Maximum Load ◽  
Lap Joints ◽  
Interface Fracture ◽  
Metal Composite ◽  
Interface Failure ◽  
Interface Shear ◽  
Nominal Strength ◽  
The University

Knowledge of the size effect on the strength of hybrid bimaterial joints of steel and fiber composites is important for new designs of large lightweight ships, large fuel-efficient aircrafts, and lightweight crashworthy automobiles. Three series of scaled geometrically similar specimens of symmetric double-lap joints with a rather broad size range (1:12) are manufactured. The specimens are tested to failure under tensile displacement-controlled loading, and at rates that ensure the peak load to be reached within approximately the same time. Two series, in which the laminate is fiberglass G-10/FR4, are tested at Northwestern University, and the third series, in which the laminate consists of NCT 301 carbon fibers, is tested at the University of Michigan. Except for the smallest specimens in test series I, all the specimens fail by propagation of interface fracture initiating at the bimaterial corner. All the specimens fail dynamically right after reaching the maximum load. This observation confirms high brittleness of the interface failure. Thus, it is not surprising that the experiments reveal a marked size effect, which leads to a 52% reduction in nominal interface shear strength. As far as the inevitable scatter permits it to see, the experimentally observed nominal strength values agree with the theoretical size effect derived in Part II of this study, where the size exponent of the theoretical large-size asymptotic power law is found to be −0.459 for series I and II, and −0.486 for series III.

Size Effect and Fracture Characteristics of Composite Laminates

1996 ◽  
Vol 118 (3) ◽  
pp. 317-324 ◽  
Author(s):  
Zdeneˇk P. Bazˇant ◽  
Isaac M. Daniel ◽  
Zhengzhi Li
Keyword(s):  
Size Effect ◽  
Composite Laminates ◽  
Process Zone ◽  
Fiber Composite ◽  
Maximum Load ◽  
Two Dimensions ◽  
Effective Length ◽  
Smooth Transition ◽  
Fracture Characteristics ◽  
Nominal Strength

Measurements of the size effect on the nominal strength of notched specimens of fiber composite laminates are reported. Tests were conducted on graphite/epoxy crossply and quasi-isotropic laminates. The specimens were rectangular strips of widths 6.4, 12.7, 25.4 and 50.8 mm (0.25, 0.50, 1.00 and 2.00 in.) geometrically similar in two dimensions. The gage lengths were 25, 51, 102 and 203 mm (1.0, 2.0, 4.0 and 8.0 in.). One set of specimens had double-edge notches and a [0/922]s crossply layup, and another set had a single-sided edge notch and a [0/±45/90]s, quasi-isotropic layup. It has been found that there is a significant size effect on the nominal strength. It approximately agrees with the size effect law proposed by Bazˇant, according to which the curve of the logarithm of the nominal strength versus the logarithm of size represents a smooth transition from a horizontal asymptote, corresponding to the strength criterion (plastic limit analysis), to an inclined asymptote of −0.5 slope, corresponding to linear elastic fracture mechanics. Optimum fits of the test results by the size effect law are obtained, and the size effect law parameters are then used to identify the material fracture characteristics, particularly the fracture energy and the effective length of the fracture process zone. Finally, the R-curves are also identified on the basis of the maximum load data. The results show that in design situations with notches or large initial traction-free cracks the size effect on the nominal strength of fiber composite laminates must be taken into account.

Structure Strength Analysis for Universal Coupling of Medium Thickness Plate Mill Based on FEM

2013 ◽  
Vol 321-324 ◽  
pp. 1794-1798
Author(s):  
Li Kun Guan ◽  
Wei Dong Liu ◽  
Ning Ning Wang
Keyword(s):  
Optimization Design ◽  
Maximum Load ◽  
Coupling Model ◽  
Strength Analysis ◽  
Plate Mill ◽  
Medium Thickness ◽  
Element Analysis ◽  
Fork Head ◽  
Structure Strength ◽  
Universal Coupling

In this paper,in view of the fork head often broken of the main drive system of a medium thickness plate mill,finite element analysis software ANSYS is used to establish universal coupling model and analyse static strength of the universal coupling, woning maximum stress value of the fork head and cross shaft at maximum load and analysing fracture reason of the fork,which could provide a theoretical basis for the cross shaft universal coupling strength analysis and structural optimization design.

scholarly journals EFFECT OF WOOD DENSITY AND SCREW LENGTH ON THE WITHDRAWAL RESISTANCE OF TROPICAL WOOD

Nativa ◽  
2018 ◽  
Vol 6 (4) ◽  
pp. 402
Author(s):  
Mariana Lopes Ribeiro ◽  
Cláudio Del Menezzi ◽  
Milton Luiz Siqueira ◽  
Rafael Rodolfo de Melo
Keyword(s):  
Wood Density ◽  
Maximum Load ◽  
Penetration Length ◽  
Tropical Wood ◽  
Strength Limit ◽  
Screw Length ◽  
Screw Penetration ◽  
Screw Withdrawal ◽  
Timber Connections ◽  
Dinizia Excelsa

EFEITO DA DENSIDADE DA MADEIRA E DO COMPRIMENTO DO PARAFUSO NA RESISTÊNCIA AO ARRANCAMENTO EM MADEIRAS TROPICAIS Na maioria das ligações os pinos metálicos estão solicitados por forças laterais, mas ocasionalmente há a necessidade da utilização de parafusos auto-atarraxantes solicitados por esforços de tração. O objetivo deste trabalho foi determinar, de maneira experimental, a resistência ao arrancamento de parafuso auto-atarraxantes em espécies de madeiras tropicais, analisando-se a influência dos seguintes fatores: densidade da madeira e comprimento de penetração do parafuso. Para isso, foram feitos testes de arrancamento com parafusos sextavados de rosca soberba com 12,7 mmde diâmetro e diferentes comprimentos de rosca e corpos-de-prova confeccionados das seguintes espécies: angelim (Dinizia excelsa), freijó (Cordia goeldiana), ipê (Tabebuia sp.), louro-vermelho (Nectandra rubra), marupá (Simarouba amara). Verificou-se que a carga máxima de arrancamento de parafuso aumenta com o aumento do comprimento do parafuso inserido na madeira e da densidade da madeira. Contudo, a ruptura do parafuso em espécies mais densas pode ocorrer, pois a carga de arrancamento ultrapassa o limite de resistência do parafuso. Dessa forma, comprimentos de parafuso menores são recomendados para madeiras mais densas.Palavras-chave: ligações mecânicas, madeiras amazônicas, parafuso auto-atarraxante. ABSTRACT: In most timber connections a metallic pin is required due to lateral forces, but occasionally self-tapping screws are required due to tensile stresses. The aim of this study was to experimentally determine the withdrawal resistance of self-tapping screws in tropical wood species by analyzing the influence of wood density and screw penetration length. For this, withdrawal resistance tests using hex lag screws of 12.7 mmdiameter and different thread lengths were performed in specimens of the following species: Angelim (Dinizia excelsa), Freijó (Cordia goeldiana), Ipê (Tabebuia sp.), Louro-vermelho (Nectandra rubra), and Marupá (Simarouba amara). It was verified that the maximum load of screw withdrawal increases with increasing screw length inserted in wood and wood density. However, screw rupture may occur in denser species because the withdrawal load exceeds the screw strength limit. Therefore, lower screw lengths are recommended for denser woods.Keywords: mechanical connections, amazon timber, self-tapping screw.

General Fishnet Statistics of Strength: Nacreous, Biomimetic, Concrete, Octet-Truss, and Other Architected or Quasibrittle Materials

2019 ◽  
Vol 87 (3) ◽  
Author(s):  
Wen Luo ◽  
Zdeněk P. Bažant
Keyword(s):  
Failure Probability ◽  
Three Dimensional ◽  
Strength Distribution ◽  
Particulate Composites ◽  
Material Microstructure ◽  
Engineering Structures ◽  
Quasibrittle Materials ◽  
Statistical Behavior ◽  
Octet Truss ◽  
Strength Models

Abstract The fishnet probabilistic model was recently developed to characterize the strength distribution of nacre-like biomimetic materials. It reveals that the unique fishnet-like connectivity of the material microstructure brings about enormous safety gain at the extremely low failure probability level of one out of a million, desired for engineering structures. The gist of the theory is that the material microstructure plays a determining role in its failure probability tail. Therefore, a carefully designed connectivity for a material microstructure not only enhances its mean strength but also significantly reduces its marginal failure risk. Here, we first show that the initially introduced series expansion and the newer formulation based on order statistics are, in the fishnet model, essentially equivalent. From that we develop a neat general form of the fishnet statistics. Then, we extend our theoretical approach to the strength distributions of architected nanomaterials such as the printed octet-truss carbon nanolattices, as well as to quasibrittle particulate composites such as concrete, and formulate a unified general fishnet statistics. We demonstrate that the octet-truss system can be physically seen and statistically treated as a union of three fishnets with three mutually orthogonal orientations. We show that the three-dimensional assembly of fishnets further enhances the tail strength at the 10−6 probability quantile, compared to two-dimensional (2D) fishnet statistics. We compare the performance of different statistical strength models by fitting of the simulated and experimental histograms data for the octet-truss nanolattice. Finally, we argue that, at the extreme lower tail of failure probability, quasibrittle materials such as concrete or fiber composites should partially exhibit the fishnet-type statistical behavior.

scholarly journals Specimen Size Effect of Interface Strength Distribution Induced by Grain Structure of Cu Line

2013 ◽  
Vol 79 (799) ◽  
pp. 354-358 ◽  
Author(s):  
Chuantong CHEN ◽  
Nobuyuki SHISHIDO ◽  
Kozo KOIWA ◽  
Shoji KAMIYA ◽  
Hisashi SATO ◽  
...  
Keyword(s):  
Size Effect ◽  
Interface Strength ◽  
Strength Distribution ◽  
Specimen Size ◽  
Grain Structure

Universal size effect of concrete specimens and effect of notch depth

2017 ◽  
Vol 3 (1) ◽  
pp. 47 ◽  
Author(s):  
Sıddık Şener ◽  
Kadir Can Şener
Keyword(s):  
Size Effect ◽  
Crack Length ◽  
Asymptotic Properties ◽  
Experimental Program ◽  
Three Point Bending ◽  
Large Size ◽  
Nominal Strength ◽  
Notch Length ◽  
Point Bend

The universal size effect law of concrete is a law that describes the dependence of nominal strength of specimens or structure on both its size and the crack (or notch) length, over the entire of interest, and exhibits the correct small and large size asymptotic properties as required. The main difficulty has been the transition of crack length from 0, in which case the size effect mode is Type 1, to deep cracks (or notches), in which case the size effect mode is Type 2 and fundamentally different from Type 1. The current study is based on recently obtained comprehensive fracture test data from three-point bending beams tested under identical conditions. In this test, the experimental program consisted of 80 three-point bend beams with 4 different depths 40, 93, 215 and 500mm, corresponding to a size range of 1:12.5. Five different relative notch lengths, a/D = 0, 0.02, 0.075, 0.15, 0.30 were cut into the beams. A total of 20 different geometries (family of beams) were tested. The present paper will use these data to analyze the effects of size, crack length. This paper presents a studying to improve the existing universal size effect law, named by Bazant, using the experimentally obtained beam strengths for various different specimen sizes and all notch depths. The updated universal size effect law is shown to fit the comprehensive data quite well.

Determination of strength distribution of quasibrittle structures from mean size effect analysis

2013 ◽  
Vol 66 ◽  
pp. 79-87 ◽  
Author(s):  
Jia-Liang Le ◽  
Augusto Cannone Falchetto ◽  
Mihai O. Marasteanu
Keyword(s):  
Size Effect ◽  
Strength Distribution ◽  
Effect Analysis ◽  
Mean Size
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