Classifications

• • G—PHYSICS
  • G01—MEASURING; TESTING
  • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
  • G01N3/00—Investigating strength properties of solid materials by application of mechanical stress
  • G01N3/56—Investigating resistance to wear or abrasion
• • G—PHYSICS
  • G01—MEASURING; TESTING
  • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
  • G01N2203/00—Investigating strength properties of solid materials by application of mechanical stress
  • G01N2203/0001—Type of application of the stress
  • G01N2203/0005—Repeated or cyclic
• • G—PHYSICS
  • G01—MEASURING; TESTING
  • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
  • G01N2203/00—Investigating strength properties of solid materials by application of mechanical stress
  • G01N2203/0058—Kind of property studied
  • G01N2203/0069—Fatigue, creep, strain-stress relations or elastic constants
  • G01N2203/0073—Fatigue
• • G—PHYSICS
  • G01—MEASURING; TESTING
  • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
  • G01N2203/00—Investigating strength properties of solid materials by application of mechanical stress
  • G01N2203/02—Details not specific for a particular testing method
  • G01N2203/0202—Control of the test
  • G01N2203/0212—Theories, calculations
  • G01N2203/0218—Calculations based on experimental data

Definitions

• the invention relates to the characterization of the fatigue strength of a part from its surface state.
• Fatigue damage is a practical problem encountered in all types of parts subjected to a cyclic loading spectrum.
• the manufacturing processes of such parts cause fluctuations in the surface properties and therefore in the behavior of the parts in fatigue.
• the fatigue resistance of mechanical parts depends in particular on their surface, where fatigue primers can appear.
• Most studies on the influence of the surface condition of a part on its fatigue behavior retain 3 parameters that can characterize it:
• Each parameter acts differently according to the material, so that it is generally possible to retain one as being the most representative for a given material.
• the most representative criterion is the geometric criterion.
• This criterion is related to the shape of the surface roughness profile generated by the machining range. It is then common practice to apply a mechanical model to the geometric parameters thus identified in order to estimate their influence on the fatigue behavior. State of the art
• the roughness parameters are calculated by the geometrical model, from a surface profile according to physical criteria or statistical criteria (see international standard ISO 4287 / 1-1984 (E / F / R) (1984)). This step, in general, is performed by a rugosimetry machine. Among the roughness parameters, those most often used to then determine the fatigue strength of the parts are:
• the factor Ks is defined as the ratio of the endurance limit of the specimen given with a certain surface roughness and the endurance limit of a test specimen whose surface state is chosen as a reference.
• C is a factor dependent on the machining.
• R is defined as being equal to 2 Rt / Sg where Sg: represents the maximum thickness of materials involved in the process of priming a fatigue crack. Stieler has shown that it is of the order of magnitude of the grain size of materials in a rotary bending test.
• Rts is the roughness of the specimen given with a certain surface roughness
• Rt is the roughness of the reference specimen
• ⁇ D is the endurance limit of the reference specimen
• ⁇ DS is the endurance limit of the test specimen considered
• n is a coefficient depending on the material.
• Brand et al (CETIM, 1980) constructed an abacus by smoothing a large number of available data, with straight lines of negative slope giving Ks (the surface state factor) as a function of the breaking strength Rm, for various values of roughness criterion Rt.
• the notch effect approach uses the classical definition of the effective stress concentration factor, Kf, which is the ratio of the endurance limit ⁇ D of a smooth specimen to the endurance limit ⁇ D of the notched test piece.
• Kf effective stress concentration factor
• This coefficient Kf is generally lower than the coefficient Theoretical studies of stress concentration Kt.
• Kt is the stress concentration factor
• ⁇ is a constant related to the material p: is the notch radius.
• This factor Kt is then used to establish an empirical relationship defining the factor Kf.
• Andrews and Sehitoglu (2000) focused on crack propagation and stress concentration factors present, distinguishing between cracks being considered short and long. They then proposed an expression of the stress concentrations taking into account a relaxation of the stress concentrations when the cuts are side by side.
• the fatigue strength of the parts can be influenced, inter alia, by the geometric profile of the surface.
• Accidents in the shape of this profile influence the initiation or propagation of fatigue cracks.
• the models that take them into account do not start from the real form of these accidents but from simplified geometrical descriptions of the profilometric measurements.
• the parameters resulting from these descriptions are numerous, but none of them makes it possible to ensure for all the types of accident a relevance of the mechanical model which uses it.
• it is wise to use one now and another, and only experience can decide a posteriori. This does not allow a characterization of the fatigue resistance without having carried out prior tests.
• the subject of the invention is a new procedure for characterizing the fatigue strength of a part as a function of its surface state, allowing to get rid of any purely geometric description of this profile (by the classical parameters such as roughness coefficients Ra, Rt, Rz, etc.) to focus on a mechanical description of the part in more direct relationship with the fatigue behavior of the part under consideration.
• the invention thus proposes a method of characterizing the fatigue strength of a part from its surface state, comprising the following steps:
• the step of determining (or raising) the data characterizing the surface profile of the zone comprises a substep of measurement of the geometric profile of this zone, in practice by any known probe device; however, it may be envisaged to use other techniques, especially purely optical, electrical, sound, thermal,
• the step of raising / determining the data characterizing this profile comprises a substep of sampling, which makes it possible to reduce the size of the storage memory required, without, however, risking completely neutralizing surface accidents; preferably, this substep of sampling is designed so as to reduce the number of data characterizing the surface profile by at least a factor of 10; however, the absence of sampling is possible if the calculation means allow it,
• the step of determining the data characterizing this profile comprises a sub-step of filtering, for example to remove the effect of the inclination or the geometry of the part (for example for a cylindrical part, the curvature related to its diameter).
• the step of determining the data characterizing this profile comprises a substep of adjustment according to the calculation model, which can guarantee the respect of the format imposed by the calculation model,
• the calculation model to which the data are applied is a finite element calculation model or its variants (XFEM, BARSOOM, ....), which corresponds to a well-controlled calculation tool; other models of calculation can however be envisaged, such as in particular the other numerical methods like the particulate numerical models, the finite or spectral differences, the integral methods, - the model of computation integrates a thickness of the part; advantageously, this thickness is at least 0.5 mm, preferably at least 1 mm below the surface of said zone, which appears to be quite sufficient to correctly estimate the stress field, whatever the surface profiles studied; this thickness can nevertheless be optimized case by case according to the state of the art,
• the calculation model determines, for each calculation element (finite element, or numerical element of the model used, etc.) stress values along two or three main axes of said zone, which allows a better estimate of the stress field than with a single axis,
• the model is applied only at least a non-zero distance from the edges of the zone of the part, for example at least 1 mm from these edges, so as to avoid the effects of edges (unless it is possible to integrate these effects in the calculation model),
• the characteristic magnitude of the fatigue behavior is a concentration coefficient of the maximum stresses, which corresponds to what is given by the current measurement chains using both a geometrical model and a mechanical model; other quantities such as the distribution of stresses in the thickness can be easily obtained from the numerical model used in the invention.
• FIG. 1 is a diagram schematizing the stages of the characterization of the fatigue strength of a part from its surface profile
• FIG. 2 is a diagram showing the roughness coefficient denoted Rz
• FIG. 3 is a diagram schematizing the steps of the method according to the invention, by analogy with the formalism used in FIG.
• FIG. 4 is an implementation diagram of one embodiment of the method of the invention.
• FIG. 5 is a diagram of a first step of implementing this method
• FIG. 6 is a graph showing the profile of a machined specimen over a length of 17.5 mm;
• FIG. 7 is a diagram of a second step of implementing the method;
• FIG. 8 is a graph showing the acquired profile as well as the modified profile
• FIG. 9 is a diagram of a third stage of implementation of the method
• FIG. 10 is a graph showing the modified profile as well as a detail thereof;
• FIG. 11 is a graph showing this modified profile, as well as this detail, broken down into finite elements;
• FIG. 12 is a diagram of a fourth implementation step
• FIG. 13 is a graph representing the local stress field
• FIG. 14 is a diagram of a fifth stage of implementation of the method.
• FIG. 15 is a graph showing the Wohler curve obtained for various specimens
• FIG. 16 is a graph showing the Wohler curve obtained for the same specimens after correction by the coefficient of stress determined by the coefficient obtained at the end of the fifth step.
• a profilometric measurement is used in a mechanical model, without going through an intermediate geometric modeling of the profile involving the determination of roughness coefficients.
• This measurement chain is shown diagrammatically in FIG. 3: the mechanical model directly uses the profiling of the profile in a mechanical model, so as to determine one or more mechanical parameters, such as stress concentration coefficients.
• step of acquiring the profile of the surface by determining (or raising) data characterizing the surface profile of a chosen zone of the part under consideration,
• Step 1 Acquire the Surface Profile
• the geometrical state of the surface is measured in this step (see Figure 5). It is determined by a measuring machine (contact or optical) of any appropriate known type, such as a probe device conforming to the standard NF-ISO 3274, June 1977, implementing the provisions of ISO - 4287 / 1984 (E / FR) 1984 already mentioned above.
• the resulting profile ie the total profile (direct or gross profile) or the primary profile (in practice, after elimination of the nominal shape of the analyzed part area, and possible application of a filter low pass) is digitally recorded and is then used in the proposed measurement chain.
• FIG. 6 shows, by way of example, the profile of the surface of a machined specimen acquired by a rugosimetry machine of the "Mahr Perthometer-PKG 120" type.
• the direct profile obtained without filter was recorded in ASCII format by an available function proposed by this roughness meter. This profile is composed of the form deviation, the undulation, the periodic or pseudoperiodic roughness (the striations and furrows) and the roughness aperiodic (tearing, tool marks and slits, tapping, etc.).
• Step 2 Process the profile
• the profile obtained in the first step is then advantageously sampled, modified and adjusted (see Figure 7).
• Sampling has the advantage of reducing the requested memory size and calculation time.
• sampling methods are possible, for example, with a fixed frequency, with an average neighborhood value, and so on.
• the profile can be modified by different filters to remove unwanted parameters such as tilt. A possible adjustment of the result may be necessary to be able to integrate this profile into the subsequent calculation model.
• FIG. 8 represents, on a much finer scale than in FIG. 6, a detail of the profile acquired during the first step, as well as this same profile after treatment.
• the processing step is performed by a calculation software.
• the sampling method is performed at a fixed frequency chosen to reduce the number of points on the order of 11000 points to about 550 points, no other modification being made.
• the heights of the profile were adjusted by removing the average of the profile and the arithmetic difference of the profile.
• the first point and / or the last point were imposed by the respect of the condition to have a height equal to zero, with a step equivalent to the sampled frequency.
• the software used in this step was the SCILAB software. Command lines are produced, and presented in Appendix A. It can be noted in the examination of Figure 8 that the profile obtained is smoothed, and some periodic or pseudoperiodic roughness and aperiodic roughness disappeared due to sampling.
• Step 3 Integrate the profile into a calculation model, here a finite element calculation model
• the modified profile is then integrated into a computational model for determining the stress field (see Figure 9). It is advantageously a finite element calculation model. Integration is different depending on the software chosen. Geometry, boundary conditions and assumptions are appropriately set so that the stress field can be calculated.
• the transition from the processed profile (FIG. 10) to the finite element decomposition (FIG. 11) was performed using the SAMCEF-Asef calculation software. It needs an input databank with a specific format generated by a text editor.
• a thickness of 5 mm was taken into consideration by imposing a plane of symmetry, which corresponds to an equivalent thickness of 10 mm in the model (on either side of the line according to which the profile has been acquired).
• the calculation has been simplified by assuming linear elastic behavior and boundary conditions representing uniformly distributed loads. The sizes and the number of meshes were limited by the available memory area and the requested computation time.
• command lines of the SCILAB software were made to generate the calculation file (databank) from the processed profile; they are presented in Appendix B.
• Step 4 Calculation of the stress field, here by finite elements
• This step is performed by finite element calculation software.
• One or more parameters are envisaged to represent the stress field thus obtained.
• FIG. 13 represents the result obtained by the implementation of the finite element calculation software SAMCEF module asef chosen (see step 3) to calculate the field of the constraints. Only the group of results between the distance 1 mm and the distance 16.5 mm was retained, to eliminate the effect of the edge (on the sections 0-1 mm and 16.5-17.5 mm), with a depth of 1 mm. They have been registered for processing in the next step. Two results (the constraints in the main axes and the coordinates of the finite element considered) were recorded with post-processing commands ("post-process") in the database. Step 5: Process the results
• Various processing can be applied here to the data from the computation step of the stress field, in order to deduce from the estimation of the stress field at least one characteristic quantity of the fatigue behavior of the part under consideration (less than explored area), such as stress concentration coefficients.
• the constraints of the field estimated in step 4 are divided by the nominal stress, so as to calculate the conventional stress concentration coefficients.
• One or more characteristic parameters of the influence of the geometrical state on the fatigue strength can then be calculated from these coefficients.
• the concentration coefficients of the maximum stresses are calculated.
• results of fatigue tests represented by the Wohler curve of FIG. 15, have been corrected by the concentration factors Kt of the maximum stresses obtained (see FIG. Figure 16). It is observed, by comparison of these figures 15 and 16, that the differences between the different surface states are largely attenuated by the correction (multiplication) by the measured Kt.
• Appendix B The Scilab Command Lines for Performing Step 3 Work
• ABRE ' ⁇ NE_groY' (( ⁇ thick - ⁇ mf_y): ⁇ ( ⁇ lm: ⁇ NE_surf)) ' ⁇ n' ; profil0,2)) // Geometry mfprintf (fd ; ' ⁇ ! ⁇ N ...
• Vn ... .DROITVa ... i 103 Item 180018002 Vn ... i 105 Item% i 80078008 Va ... i 107 Item 8003 to 8005 Vn ... i 109 Item 8009 to 801 IVn ... i 111 Number 8003 IVn ... i 112 Point% i 8009 Vn ... i 113 Point 8005800280088011 Vn ... V! Loading line Vn ... i 121 Item 80038005 V! On the left Vn ... i 122 Point 80098011 ⁇ ! On the right Vn ... i 123 Point 80058011 V! Below Vn'j + 1 d + 1 d + 1)
• VMwidth in horizontal (X axis) ⁇ n ... modifies Line 111 113 ⁇ t Element ( ⁇ NE_sec2: 3) distribute 3 6 Vn ... modifies Line 112 115 ⁇ t Element ( ⁇ NE_sec2: 3) distribute 2 6 Vn ... modifies Line 1 ⁇ t Element ( ⁇ NE_surf) Vn ... modifies Line 114 ⁇ t Element ( ⁇ NE_surf) ⁇ n ... VIMalize in vertical (Y axis) ⁇ n ... modifies Line 107 103 105 109 ⁇ t Element ( ⁇ NE_finY) ⁇ n ... modify Line 108 104 106 110 ⁇ t Element ( ⁇ NE_groY: 3) distribute 2 6 ⁇ n .. ⁇ n ...
• VIMautomatic ⁇ n deg 1 ⁇ n ... cl 1 c2105106 c3114 c4104103 ⁇ n ... mesh 1 transfinite ⁇ n ... cl 111 c2103104 c3113 c4108107 ⁇ n ... mesh 2 transfinite ⁇ n ... cl 112 c2 109 110 c3 115 c4 106 105 ⁇ n ... mesh 3 transfinite ⁇ n ... ⁇ n ... ⁇ ! Vn ...
• Group 1 nodes name% cResultat_zone% c ⁇ n ... STRUCTURE BOX $ ⁇ n ... XI (1000) XS (Wlm-1000) $ Vn ... YI (100) YS (-1000) $ ⁇ n .. ZI - (l) ZS (l) ⁇ n ...

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