Bracket crack

FAILS. A 1.27 mm through crack at the edge of the 8 mm hole at (91.7, -3.6, 2.5) fails after about 86,219 cycles in a typical part. One part in ten fails by 55,144 cycles and one in a hundred by 37,968. 68% of parts fail before the 100000 cycle target (allowed 1%). Confidence: medium. crack path: 10 solved cracks from 0.865 to 9.17 mm, ended by a step that could not be meshed or solved (gmsh could not mesh the part with the crack in it (_build took longer than 180 s). Past 9.17 mm K is carried on as the square root of size to the far side of the wall at 10.3 mm, and 0.388% of the nominal life rests on that estimatenominal life: 86,219 cyclesB10: 55,144 cyclesB1: 37,968 cyclesfail before target: 68%inspect every: 43,110 cycles Checks:  [pass] SIF mesh convergence: largest K at the starting crack 7.17 -> 7.17 MPa sqrt(m) with front elements of 0.0926 and 0.0618 mm, last change 0.1%  [pass] hand calculation: the edge crack weight function (Glinka and Shen) over the uncracked stress along the crack gives 7.77 MPa sqrt(m) for the 0.865 mm starting crack; the finite element K is 7.17 (-7.7%)  [pass] force balance: reactions balance the loads to 4.9e-05% (forces) and 7.1e-06% (moments)  [pass] integration step: nominal life 86,212 cycles with 200 steps in crack size and 86,219 with 400, 0.0086% apart  [pass] Monte Carlo samples: B1 37,968 cycles from 20,000 parts, 90% sampling band 37,177 to 38,480 (within 1.7%), and 37,596 from the first half of the parts (0.98% off)  [warn] crack path: 10 solved cracks from 0.865 to 9.17 mm, ended by a step that could not be meshed or solved (gmsh could not mesh the part with the crack in it (_build took longer than 180 s). Past 9.17 mm K is carried on as the square root of size to the far side of the wall at 10.3 mm, and 0.388% of the nominal life rests on that estimate Assumptions:  - Aluminum 7075-T6: NASGRO growth with C 1.16e-07 mm/cycle and n 3.7, threshold 1.8 MPa sqrt(m) at R = 0, toughness 29 MPa sqrt(m). Source: Paris fit and K_Ic from Dowling, Mechanical Behavior of Materials, 4th ed. (2013), Table 11.2 (Walker C0 and m); threshold 1.8 MPa sqrt(m), the IIW lower bound for aluminium at R = 0 (Hobbacher 2016).  - Loads cycle as constant amplitude between 0.1 and 1 of the load (R = 0.1), with the loads given as the peak.  - The crack plane at the start is normal to the largest principal stress at the origin, 190 MPa before the crack.  - The path starts from a crack 0.68 times the size given, the smallest tenth of the starting flaws sampled; smaller cracks follow the uncracked stress through the edge crack weight function, matched to the first solved K.  - K for growth combines the three modes by energy, sqrt(K_I^2 + K_II^2 + K_III^2 / (1 - nu)), and the turn uses K_I and K_II only (maximum tangential stress).  - Failure is K_max reaching the toughness or the average stress over the remaining ligament reaching the flow stress, 538 MPa, the mean of yield and tensile strength. Bending in the ligament is not counted, so net section yield is approximate.  - Parts scatter as lognormal: starting flaw 0.3, growth coefficient 0.25, load 0.05, toughness 0.07 (standard deviations of the logarithm). One part's failure cycle cannot be predicted; the percentiles describe many parts.  - The Monte Carlo keeps the solved path's shape and changes only how fast a part's crack travels along it.  - Linear elastic fracture mechanics: crack tip plasticity, crack face contact and environment are not modeled. Suggested fixes:  - Lower the stress at the crack's origin by 20%: Growth goes as the stress range to the power 3.7, so lowering the stress where the crack starts by 20% (a larger radius, a thicker section or a smaller load) brings B1 to the 100000 cycle target.  - Use Mild steel (ASTM A36): With Mild steel (ASTM A36)'s crack growth constants on the same path, B1 is 1.46e+06 cycles against 38,058 now. Its stiffness does not change K under the same loads, but check its strength and weight with a strength study.  - Use Stainless steel 304 (annealed): With Stainless steel 304 (annealed)'s crack growth constants on the same path, B1 is 1.04e+06 cycles against 38,058 now. Its stiffness does not change K under the same loads, but check its strength and weight with a strength study.  - Inspect every 43,110 cycles: Damage tolerance practice: the first inspection at half the nominal life from the starting crack (43,110 cycles), then every half of the life from a 1.27 mm crack, the size an inspection is taken to find reliably, to failure (86,219 cycles). Images: path: images/path.png, growth: images/growth.png, life: images/life.pngReport: report.html

HOLDS. Peak 320 MPa on the 6 mm inside fillet (face 3) at (34.5, -14.2, 3.02), safety factor 1.57 against yield (target 1.5). Confidence: high. passed mesh convergence, force balance, hand calculation, singularities, bolt bearing, units and sanityMax deflection 0.415 mm at (104, -1.33e-14, 5).Material Aluminum 7075-T6, limit 503 MPa; mass 47.6 g.Loads: 4 kN 0.866,0.5,0 bearing @ hole d=8. Fixtures: bolt holes d=6.6. Checks:  [pass] mesh convergence: von Mises stress settled: 304 -> 323 -> 320 MPa over 3 meshes, last change 0.9%  [pass] force balance: reactions balance the loads to 2.6e-05% (forces) and 3.3e-06% (moments)  [pass] hand calculation: beam theory through the critical section gives 190 MPa nominal; FEA peak is 1.69x that, a stress concentration of about 1.7 from the local shape  [pass] singularities: no sharp corner or support artifact is above the reported stress  [pass] bolt bearing: worst hole of fix1 (d 6.6 mm) carries 5226 N sideways and 79.9 N along its axis; bearing stress 158 MPa, safety factor 4.77 on bearing  [pass] units and sanity: part 116 mm across, peak strain 0.0045, max deflection 0.415 mm (0.36% of size): all plausible Assumptions:  - Linear elastic material and small deflections (no yielding redistribution, no buckling).  - Aluminum 7075-T6: E 71700 MPa, Poisson 0.33, von Mises vs yield 503 MPa (ASM Aerospace Specification Metals, Aluminum 7075-T6).  - Loads are static and applied all at once; no impact, vibration or fatigue.  - Wrought metal treated as isotropic; rolled, drawn or extruded stock is close to it at yield.  - Bolted holes are rigidly held over the hole and a washer sized ring (twice the hole radius).  - Bolt loads press on the loaded half of each hole with a cosine distribution.  - Contact between separate parts, friction and preload are not modeled. Images: stress: images/stress.png, zoom: images/zoom.png, safety: images/safety.png, deformed: images/deformed.png, convergence: images/convergence.pngReport: report.html