- How is the relative stress gradiant calculated in FEMFAT?
- How do I utitlize BREAK correctly?
- Is there a possibility to consider constant stresses?
- What are the effects of the individual surface treatments?
- What inferences concerning the fatigue life can be made based on the endurance safety factors?

Calculation of the relative stress gradient is performed automatically on the basis of Mises equivalent stresses. Here, the respective neighboring nodes for each node in the analysis group are searched for. By forming differential stresses, divided by the distance, the absolute gradient to each neighboring node is obtained. The maximum of all these calculated gradients is then selected and related to the local amplitude stress. The resultant relative stress gradient forms the basis for calculation of the support effect.

**Special cases**

For shell structures subjected to pure bending loads, or one-layer solid models, a stress gradient of 0 would be falsely obtained, because the equivalent stress on the top and bottom is identical. Therefore, the stress tensor directly at the neighboring node is not evaluated in order to generate an equivalent stress, but at a distance of 1/100th to the neighboring node. By using this stress, which is located very close to the current node, the stress decrease can now be correctly considered. A further special case is given by midside nodes in parabolic elements on component surfaces without neighboring nodes in the interior of the component. The stress gradient perpendicular to the surface can thus not be correctly considered. The stress gradient at the midside nodes is therefore not calculated directly; in an initial computation the gradient at all corner nodes is calculated. In the second computation loop, the absolute stress gradient at midside nodes is determined by averaging the absolute gradient at the corresponding neighboring corner nodes and then relating them to the local Mises stress.

**Procedure in MAX**

In **FEMFAT basic**, the relative stress gradient is always obtained from the amplitude stress dataset, as the support effect is always in relation to the dynamic load component.

In **FEMFAT max**, in contrast, the dynamic component is not defined by the user, but must first be determined in FEMFAT, for instance by Rainflow counting of an equivalent stress in cutting plane:

• Calculations are performed with a stress gradient invariant over time (“representative”).

• In ChannelMAX, the relative stress gradients are calculated separately for each unit load case in analogy to **FEMFAT basic**. A weighted average is then formed via the load channels. The dominating load channels therefore have a greater influence on the stress gradient result.

• In TransMAX the following method is available:

Maximum stress difference (default):

•By combination of two time points from the load history the local pair with the biggest stress difference is searched, i.e. the greatest dynamic component. From this the relative stress gradient is subsequently obtained in analogy to **FEMFAT basic**.

**FEMFAT ****break **is a very practical tool for computing static safety factors from linear-elastic FEM stresses. For abrupt, infrequent loads (e.g. transmission jump starting, chassis-verge stone contact) it is recommended to perform a FEMFAT break analysis prior to the fatigue analysis. If an insufficient static safety factor results here (safety factor smaller than 1.0) the component is statically underdesigned.

**The static safety factor is used to evaluate the local elongation capacity of the material until cracking under a monotonic load.**

Please note that FEMFAT break cannot assess the global failure (fracturing, breakage) of a component (unless the material is highly brittle), but only the local material failure due to insufficient ductility. This means that initial damage (small crack) may be caused by high load peaks, which leads to further crack growth under subsequent operating loads, and finally to failure. In addition, it is assumed that the constant load is not applied highly dynamically; i.e. BREAK does not take strain rate effects into consideration. Influences in the BREAK module the notch influence is taken into consideration by means of the relative stress gradient. Required material parameters:

•Young’s modulus

•Static tensile strength Rm

•Static compressive strength

•Static shear strength

•Static elongation at rupture A5

Image: Ratio of notch tensile strength to tensile strength as a function of the stress concentration factor and Vickers hardness, as a measure for ductility.

The ratio of bending to tensile strength defines the impact of the gradient influence; i.e. the greater the ratio, the greater the strengthening and the smaller the (negative) notch influence on the static component strength. Under static loads, the notch influence may even reverse, in contrast to cyclic loads. That is, it may have a positive influence on component strength as a function of the ductility of the material, see diagram (source: Systematische Beurteilung technischer Schadensfälle, third revised/extended edition, G. Lange, Informationsgesellschaft Verlag). The cause of this is that a ductile material only begins to yield under higher loads due to the multi-axial stress state in the notch. Brittle failure dominates in a brittle material.

**Evaluation Method **

By default the maximum principal stress is adopted as the relevant value for gray cast iron and a modified Mises stress taking the shear strength into consideration for all other materials. The ultimate tensile or compressive strength is adopted for gray cast iron, as a function of the prevalent principal normal stress components. Effective failure strength is computed for ductile materials by interpolation. The static elongation of rupture is very important in BREAK, because it is used to compute the maximum local notch strength. That is, the static safety factor in sharp notches increases in direct proportion to the static elongation. In addition, it should be noted that the static elongation in the component may drop locally, in particular in light metals and for poor casting processes.

Since FEMFAT version 5.0 BREAK is also available in MAX. There at each node a separate static safety assessment is performed for each time point. At the currently analyzed node the time point with minimum static safety factor is assumed to be critical and the corresponding results are written into the dma- and pro-file.

FEMFAT basic provides the possibility of reading a third load case, designated as constant stress (σc), at the given amplitude and mean stress (σa, σm). These could arise from internal stresses or screw preloadings. When the constant stress effect (influence factors -> general factors; Fig. 1) is activated, the constant stress is included in the mean stress during the calculation. The difference with regard to the mean stress data set is in the definition of the load spectra, where only the mean stress is scaled with the “mean stress factor” (F_M) for each step. In the case of the fatigue strength analysis, the constant tensile stress with the R = const. option (one of the FKM overload situations) is taken into account as a shift to the right in the Haigh diagram (Fig. 2).

Fig. 1

Fig. 2

Besides the material, component geometry and stress conditions, the manufacturing process has a major influence on the fatigue behavior of a component.

In FEMFAT the following surface treatments are available:

•Shot peening (acc. to FKM, Eurocode or BS),

•Rolling (to FKM),

•Carburizing (to FKM),

•Nitriding (to FKM),

Here, the condition prior to nitriding can also be taken into consideration: Tempered or normalized

•Inductive hardening (to FKM),

•Flame hardening (to FKM).

"Node properties menu" for the current group

For these treatments it is important that the Technological size at 3D nodes is given in "Node properties" (see image). This technological size is automatically determined from the mean shell thicknesses for shell structures. For example, the technological size is the wall thickness of a tube or the diameter of a shaft at the point where the surface treatment is carried out. Other influences, such as the relative stress gradient and the material strength are automatically taken into consideration by FEMFAT.

The Surface treatment factor provides a good option for incorporating experiences from testing into analysis. This directly alters the local endurance stress limit.

One common technological influence is the Surface roughness, which can be assigned to the current group. The S/N curves of the material data are generally defined for a smooth, un-notched specimen for alternating tensile-compressive loading. This means that a change in the surface roughness also changes the endurance stress limit, the slope and the endurance cycle limit of the local S/N curve at the node, including as a function of the material itself. In the methods listed under "Influence factors" one can also select between mean roughness depth Rz (to TGL or FKM) or the maximum roughness depth Rt (IABG) of the assessed component surface. The former TGL Standard - replaced by the FKM Guideline in 1994 - is no longer recommended.

FEMFAT also includes an option for taking the Tempering condition into consideration for tempered steels. If the tempering condition changes (= new ultimate tensile strength) all governing material parameters are adapted to the new tempering condition. Following this, do not forget to activate the process influences in "Influence factors" (surface roughness, technological parameter influence, tempering influence...)!

Often, after an endurance safety analysis has been made, the additional question arises of how many cycles the component can sustain under the load which is to be applied. In the case of single-level load spectra, this question can be answered by means of a simple conversion between safety factor and fatigue life:

If the safety factor is less than 1, in order to calculate the sustainable number of cycles N, the degree of utilization (= reciprocal of the safety factor 1/SFA) is raised to the power of the negative slope k of the (local) S/N curve and multiplied by the (local) endurance cycle limit ND:

N =ND* (1/SFA ) -k

If the safety factor is greater than 1, the conversion depends on the Miner rule used:

By the way, this conversion can be carried out very conveniently using the FEMFAT Results Manager in which the above-mentioned case differentiation for the safety factor can be made automatically with the help of the formula Editor.