3. Operands common to all options#
3.1. Operand METHODE_PROPA#
♦ METHODE_PROPA =/”SIMPLEXE”,
/”UPWIND”, /”MAILLAGE”, /”INITIALISATION”, /”GEOMETRIQUE”,
Three methods are available to cause a crack defined with the X- FEM method to propagate:
Methods based on a fast marching algorithm
(METHODE_PROPA =” UPWIND “): a discretization of the Eikonal equation is solved to reset lsn and lst. The use of the auxiliary grid is essential for irregular meshes. For more details concerning the algorithms relating to this method, we can refer to the reference documentation [R7.02.12].
(METHODE_PROPA =” SIMPLEXE “): Robust method, which can be applied to any meshes. For more details concerning the algorithms relating to this method, we can refer to the reference documentation [R7.02.12].
a method using an intermediate surface mesh of the crack lip (METHODE_PROPA =” MAILLAGE “): this method is available in 2D and 3D for all types of finite elements.
The initial crack must also be defined using a mesh, with specific naming rules. For example in 3D, the background is called \(\text{FOND\_0}\) and contains the nodes \(\text{NXA1}\), \(\text{NXB1}\),…; the lip is called \(\text{FISS\_0}\) and contains the surface meshes \(\text{MXA1}\), \(\text{MXB1}\),…; the surface mesh \(\text{MXA1}\) contains the nodes \(\text{NXA0}\), \(\text{NXB0}\), \(\text{NXA1}\) and \(\text{NXB1}\).
a method using a purely geometric approach (METHODE_PROPA =” GEOMETRIQUE “): this method using a vector propagation of the crack background and its local base as well as an estimate of the distances in relation to the latter in this local base is available in 2D and 3D for all types of finite elements without any restrictions.
To facilitate the definition of this initial crack in the most usual cases (half-straight crack (in 2D) or plane with a rectilinear bottom (in 3D)), it is necessary to use the “INITIALISATION” method.
Note on the different methods:
The method of projection onto an intermediate mesh is for its part more similar, but it makes it possible to obtain very satisfactory results, especially for propagations in pure I mode.
Fast marching methods are robust and give very satisfactory results for mixed mode propagations. The simplex method does not require an auxiliary grid.
The purely geometric method is a method which does not require an auxiliary grid and offers good performance.
3.2. Operand OPERATION#
# If METHODE_PROPA = 'GEOMETRIQUE'
◊ OPERATION =/”RIEN” [DEFAUT] /”DETEC_COHESIF” /”PROPA_COHESIF”
This keyword defines the nature of the operation required when updating the crack:
If “RIEN”, we want a classical propagation of normal and tangent level-sets according to a certain angle and a certain advance. This is the operation to be selected in the absence of cohesive forces.
The “DETEC_COHESIF” operation performs a front detection by post-processing a result with cohesive forces. Given a possible cracking surface, on which cohesion forces are defined, it makes it possible to detect the new position of the propagation front, by post-processing the result, which must be given under the keyword RESULTAT. So it’s a tangent level-set update only.
The “PROPA_COHESIF” operation extends the possible cracking area by an angle given as an argument in TABLE, and by a uniform length specified by DA_MAX. Once the direction of propagation has been determined, it is a question of extending the possible cracking zone in order to carry out the next mechanical calculation. This extension must be done over a length greater than the effective advance of the crack. This can be quantified by simple dimensional analysis, and must be verified retrospectively during the calculation.
Crack propagation algorithms with cohesive elements are described in the reference documentation [R7.02.19].
3.3. Keyword LOI_PROPA#
# If (METHODE_PROPA =” SIMPLEXE “or” UPWIND “or” “or” GEOMETRIQUE “and RAFF_MAIL =” NON”)
# or (METHODE_PROPA =' MAILLAGE 'or' INITIALISATION ')
♦ LOI_PROPA = _F (
♦ LOI = /” PARIS “, # If LOI =” PARIS “ ♦ M =m, [R] ♦ C=c, [R] ◊ DELTA_K_SEUIL =/0. [DEFAUT] /val_threshold, [R] # End yes
♦ MATER = my, [subdue]),
The keyword factor LOI_PROPA defines the propagation law used.
For the moment, the only law available is a Paris law, in the following form:
\(\frac{\mathit{da}}{\mathit{dN}}=\mathit{C.}{(\Delta {K}_{\mathit{eq}}-\Delta {K}_{\mathit{seuil}})}^{m}\)
The coefficients \(C\) and \(m\) of this law must be entered. The propagation threshold \(\Delta {K}_{\mathit{seuil}}\) is adjustable via the optional parameter DELTA_K_SEUIL, whose value by default is 0. In case \(\Delta {K}_{\mathit{eq}}<\Delta {K}_{\mathit{seuil}}\), the progress is zero.
Note:
For now all cracks in the model must propagate in the same material. In fact, only one material can be given and it is used for all the cracks in the model.
In addition, the Paris law does not allow the crack propagation threshold to be considered.
Attention:
The constants of the law of propagation must be given in such a way that the unit of the rate of progression \(\mathit{da}\mathrm{/}\mathit{dN}\) is equal to \(L\mathrm{/}\mathit{cycles}\) , where \(L\) is the unit used in the model for length.
3.4. Operand RESULTAT#
# If OPERATION =” DETEC_COHESIF “
♦ RESULAT = res, [evol_noli]
The aim is to provide the calculation result of STAT_NON_LINE whose field of internal variables of the cohesive law will make it possible to determine the position of the new propagation front.
3.5. Operand DA_MAX#
♦ DA_MAX = da, [R]
In the case where there is only one crack in the mo model, this operand defines the maximum advance of the crack.
In the case where there are several cracks in the mo model, this operand defines the maximum advance of the crack that propagates more quickly. The number of fatigue cycles is calculated using the speed of the point at the bottom of the crack that propagates the fastest. This number of cycles is used for all cracks in the model.
If OPERATION =” PROPA_COHESIF “, this keyword defines the uniform length by which to extend the new possible cracking surface in preparation for the next propagation step.
3.6. Keyword factor COMP_LINE#
# If TEST_MAIL =” NON “,
♦ COMP_LINE = _F (♦ COEF_MULT_MINI = cmin, [R]
),
Parameters COEF_MULT_MINI and COEF_MULT_MAXI of operand COMP_LINE define the minimum and maximum loading conditions for the fatigue cycle. The two values are the constants by which the loads in the reference configuration must be multiplied to obtain the minimum and maximum loading conditions for the fatigue cycle. So if the selected reference configuration coincides with the minimum or maximum load condition, the value of COEF_MULT_MINI or COEF_MULT_MAXI, respectively, is equal to 1.
3.7. Keyword factor CRIT_ANGL_BIFURCATION#
◊ CRIT_ANGL_BIFURCATION =/'SITT_MAX' [DEFAUT]
/”SITT_MAX_DEVER”
/”K1_ MAX “
/”K2_ NUL “ /”PLAN” /”ANGLE_IMPO”
/”ANGLE_IMPO_GAMMA”
/”ANGLE_IMPO_BETA_GAMMA”
This operand makes it possible to choose the criterion for calculating the angle of bifurcation:
“SITT_MAX”: maximum circumferential stress criterion (Maximal Hoop Stress criterion, [R7.02.05 §2.5.2]) this is the criterion by default. It is calculated from the values of K1 and K2. It is available in 2D and 3D.
“SITT_MAX_DEVER”: criterion of the maximum circumferential stress taking into account KIII [R7.02.05 §2.5.2] and taking into account the discharge rotation [R7.02.13 §2.1]. It is calculated from the values of K1, K2, and K3 and only available in 3D.
“K1_ MAX “, “K2_ NUL”: criteria of Amestoy, Bui and Dang-Van [R7.02.05 §2.5.1]. These 2 criteria are only available in 2D. The angle is given to within 10 degrees. Attention, we note that the criterion “K2_ NUL “does not work for an angle greater than 60°.
“PLAN”: defines a zero angle corresponding to a plane propagation.
“ANGL_IMPO”: allows you to choose an angle previously calculated. In this case, the angle given in column BETA of the input table is taken as an angle (table given under the TABLE keyword) and the dump rotation is not activated. Therefore, to do this, the PROPA_FISS input table must contain a BETA column.
“ANGLE_IMPO_GAMMA”: allows you to choose a previously calculated angle of discharge. In this case, the angle of discharge is taken from the angle given in column GAMMA of the input table (table given under the keyword TABLE) and the branch angle is calculated [R7.02.13§2.1]. Therefore, to do this, the PROPA_FISS input table must contain a GAMMA column. The angle of discharge BETA is calculated by the operator POST_RUPTURE, in the configuration CRITERE = SITT_MAX_DEVER [U4.82.04].
“ANGLE_IMPO_BETA_GAMMA”: allows you to choose branch and discharge angles previously calculated. In this case we take BETA and GAMMA as branch and discharge angles respectively and given in the input table (under the keyword TABLE). To do this, the input table must contain a column BETA and a column GAMMA of the same size.
Note:
The possibility of imposing the branch angle BETA and then deducing the discharge angle GAMMA is not in accordance with the model. In fact, the calculation of GAMMA requires knowledge of the stress intensity factors that cannot be found from the sole data of the branch angle BETA.
3.8. Operand INFO#
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Print on the file “MESSAGE”
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printing on the file “MESSAGE”
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Print on the file “MESSAGE”
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