2。2。Fracture analysis, mechanical tests and metallographic   analysis

Two of the fractured bolts, camshaft pieces as well as bolts from the remaining connecting rods were selected for labo- ratory analysis。 Those analyses consisted of low magnification and scanning electronic microscopy (SEM) observation of the fracture surface, hardness, tensile tests and metallographic characterization。 Hardness was performed over the flat shank of some selected bolts using the Rockwell C scale (HRC)。 Tensile tests were performed with a MTS 810 (MTS Corporation, Eden Prairie, MN)。 Metallographic analyses were done in two selected bolts: one broken during the failure, other during tensile test。

2。3。Numerical modeling

The assembly between connecting rod and bolts was finite element modeled, in order to analyze the correlation be- tween the tightening force, the external in service loads and the resulting stress magnitude in the bolt shank。 The net generation, boundary conditions as well as numerical analysis were done using commercial software。 The assembly con- sists of bolts, connecting rod body, connecting rod cap and a rigid shell used to distribute external load at the connecting rod cap。 The connecting rod has 36 mm width and 80 mm crankshaft diameter。 The assembly was simplified utilizing two planes of symmetry, to facilitate the net generation and decrease calculation time。 Fig。 2 shows a quarter of assembly, including boundary conditions and net generated。 The bolt net was refined at fracture plane, which is the site in analysis。 Nut and head interface sites also were refined。 The parts were considered isotropic and homogeneous and all simulations were in the linear elastic regime。 Table 1 lists net characteristics for each part。 Constitutive properties assumed for all elements, excluding the rigid shell, were 200 GPa Young modulus and 0。3 Poisson coefficient。 Tightening force was sim- ulated according to interference technique, which is present in the software package。 It consists in assess the strains in the bolt; taking into account force, area and elastic module。 Tightening force is that normal to the bolt axis as result of the tightening torque。 The torque applied in the bolt (T) is related to the tightening force (F), the bolt nominal diameter

(d) and a nut factor or torque coefficient (k) according to Eq。 (1)。 The literature indicates a nut factor k = 0。2 is a  general

good estimative [8,9]。

T ¼ F dk ð1Þ

The displacement due to the force is imposed as interference in the simulated assembly。 The faces in interference are automatically adjusted pondering the stiffness differences between the bolt and the connecting rod, approaching the real situation。 Considering 100 N m torque, 11。1 mm nominal bolt diameter and 0。2 torque coefficient, the resulting tightening force (Fa) is 45 kN。 Table 2 shows three magnitudes of simulated forces (Fa) and the respective interferences。 They were sim- ulated to demonstrate the expected decrease of stress amplitude with increasing tightening force。 The highest magnitude 60 kN shall be near the yield strength of the bolt。 From this first analysis it is possible to obtain the normal stress due to  bolt

Fig。 1。 General view of the bolts collected for mechanical tests。 Whitworth UNF7/16 20 threads per inch with 12 mm diameter shank and grooves lengthwise。

Fig。 2。  Connecting rod–bolt assembly, boundary conditions and net generated。

Table 1

Net characteristics of four parts of the   model。

Part No of elements No of nodes Element type

Bolt 3672 5044